{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "375719f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff2426b0",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "## Overview\n",
    "    > For linear regression model, 4 different approches are listed below\n",
    "    1. by matrix formula\n",
    "    2. by Batch Gradient Descent\n",
    "    3. by Stochastic Gradient Descent\n",
    "    4. by Mini-batch Gradient Descent\n",
    "## Formula\n",
    "    > model formula\n",
    "$$\n",
    "    \\hat Y = \\theta^T \\cdot X\n",
    "$$\n",
    "    \n",
    "    > cost function - RMSE\n",
    "$$\n",
    "    MSE = \\frac{1}{m}\\sum_{i}^{m}{{(Y - \\theta^T \\cdot X)}^2}\n",
    "$$\n",
    "\n",
    "    > optimized result\n",
    "$$\n",
    "    \\theta = {(X^TX)}^{-1}X^TY\n",
    "$$\n",
    "\n",
    "    > sklearn.linear_model could reach this by calling LinearRegression class\n",
    "    > for sklearn, intercept_ is bias term, corresponding to all ones column\n",
    "    > the rest parameters are stored in coef_, its number depends on features number in X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "393c5c19-572e-4dd8-8c42-a5fc51cbc999",
   "metadata": {},
   "source": [
    "## Data Generation\n",
    "$$\n",
    "    y = 3 + 4x + \\epsilon\n",
    "$$\n",
    "\n",
    "<center>* where $\\epsilon \\sim \\mathcal N (0,1)$</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "e0e9bbbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# generate linear data with random noises\n",
    "X_raw = np.random.rand(100,1)\n",
    "X = np.sort(X_raw,axis=0)\n",
    "y = 3 + 4 * X + np.random.randn(100,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43d8c09e-31cc-46e9-9f2b-450b92e04d88",
   "metadata": {},
   "source": [
    "## Closed Form\n",
    "\n",
    "$$\n",
    "    \\theta = {(X^TX)}^{-1}X^TY\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "fcf565a8-72a3-47f0-9dec-965ec00d5e94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.67523951],\n",
       "       [4.33757984]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_b = np.c_[np.ones(len(X)),X]\n",
    "xtx = np.dot(X_b.T,X_b)\n",
    "xty = np.dot(X_b.T,y)\n",
    "theta = np.dot(np.linalg.inv(xtx),xty)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "a5c00d96-283d-4e1f-96d6-f785119b67c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import warnings\n",
    "\n",
    "y_cf = theta[0] + X * theta[1]\n",
    "%matplotlib inline\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "fig,ax = plt.subplots(1,1,facecolor=\"whitesmoke\",edgecolor=\"grey\",dpi=80)\n",
    "ax.scatter(X,y,marker=\"*\",s=4.5,color=\"red\",label=\"raw data\")\n",
    "ax.plot(X,y_cf,lw=.75,ls='--',color='blue',label=\"prediction\")\n",
    "ax.legend(loc=\"upper left\",fontsize=7.5)\n",
    "ax.grid(alpha=.45)\n",
    "fig.suptitle(\"closed form of linear regression\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3521f91",
   "metadata": {},
   "source": [
    "## GD\n",
    "BGD and SGD work under the same concept, which is updating parameter vector with gradient of cost function with respect to parameter vector <br>\n",
    "\n",
    "the difference lies in training data selection. BGD will take all data into calculation, which means that data matrix is of size (m*n), while SGD only takes one random data point for training, that is a single (1 \\* n) vector, and for the purpose of preventing over-striding which would possibly leads to divergence, we introduce learning rate to fine-tune gradient for each sgd iteration. We always tends to gradually decreate learning rate with training progressing on. This process is also called simulated annealing.<br>\n",
    "\n",
    "Mini-batch GD is of the same manner, which slightly increases number of data points in each iteration. Make sure to distingush term iteration and epoch. <br>\n",
    "\n",
    "1. BGD is intrinsically embedded in <font color=sapphire><b>LinearRegressor in sklearn.linear_model</b></font>, <br>\n",
    "2. SGD could be found in <font color=sapphire><b>sklearn.linear_model.SGDRegressor</b></font>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7841718d",
   "metadata": {},
   "source": [
    "    > formula for gradient\n",
    "$$\n",
    "        \\nabla_{\\theta}MSE(\\theta) = \\frac{2}{m}X^T\\cdot(X\\cdot\\theta - y)\n",
    "$$\n",
    "\n",
    "    > formulat for paramter vector update\n",
    "$$\n",
    "        \\theta^{(next \\space step)} = \\theta - \\eta \\cdot \\nabla_{\\theta} MSE(\\theta)\n",
    "$$\n",
    "\n",
    "    > simulated annealing formula\n",
    "$$\n",
    "    \\eta = \\frac{t_0}{f(epoch)+ t_1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7454fdd6-0e55-4a06-8802-f564d5ed0987",
   "metadata": {},
   "source": [
    "### BGD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "e172a744-db9b-4481-951d-73a9083bc9b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.67523951] [4.33757984]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 512x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X,y)\n",
    "intercept = lin_reg.intercept_\n",
    "slop = lin_reg.coef_\n",
    "\n",
    "fig, ax = plt.subplots(1,1,facecolor='whitesmoke',edgecolor='gray',dpi=80)\n",
    "scatter = ax.scatter(X, y, s=4.5,marker=\"*\",color='red',label='raw')\n",
    "linear = ax.plot(X,intercept+slop*X,lw=.75,ls=\"--\",color='blue', label='predict')\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.grid(alpha=0.4)\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\")\n",
    "print(intercept, slop[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf813d7c-b168-4ab2-a833-3fa7ff82536e",
   "metadata": {},
   "source": [
    "### SGD "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "bfd6716a-6fd6-4e64-9a79-6c6c793db07f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.6460994 , 3.20109989])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "sgd_reg = SGDRegressor()\n",
    "sgd_reg.fit(X_b,y.reshape(-1,1))\n",
    "sgd_reg.coef_\n",
    "\n",
    "fig, ax = plt.subplots(1,1,facecolor='whitesmoke',edgecolor='gray',dpi=80)\n",
    "scatter = ax.scatter(X, y, s=4.5,marker=\"*\",color='red',label='raw')\n",
    "linear = ax.plot(X,intercept+slop*X,lw=.75,ls=\"--\",color='blue', label='predict')\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.grid(alpha=0.4)\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\")\n",
    "print(intercept, slop[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7a1baf4-f6e1-41f8-a657-5657b9d833f5",
   "metadata": {},
   "source": [
    "### SGD under-the-hood\n",
    "\n",
    "Due to fact that no intermediate params are stored and provided in sklearn packages, we need to restore SGD whole process and see how params as well as mse goes during each epoch. Note that with each epoch model only takes one data point as trining sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b553832b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 0: \n",
      "[[3.92039694]\n",
      " [2.2959627 ]]\n",
      "============================\n",
      "epoch 40: \n",
      "[[3.14196678]\n",
      " [3.63902   ]]\n",
      "============================\n",
      "epoch 80: \n",
      "[[3.15055455]\n",
      " [3.67271141]]\n",
      "============================\n",
      "epoch 120: \n",
      "[[3.11465892]\n",
      " [3.69219009]]\n",
      "============================\n",
      "epoch 160: \n",
      "[[3.13983845]\n",
      " [3.72524115]]\n",
      "============================\n",
      "epoch 200: \n",
      "[[3.09265185]\n",
      " [3.7245936 ]]\n",
      "============================\n",
      "epoch 240: \n",
      "[[3.10505999]\n",
      " [3.74223784]]\n",
      "============================\n",
      "epoch 280: \n",
      "[[3.10005899]\n",
      " [3.75368278]]\n",
      "============================\n",
      "epoch 320: \n",
      "[[3.07853424]\n",
      " [3.7458653 ]]\n",
      "============================\n",
      "epoch 360: \n",
      "[[3.11069137]\n",
      " [3.76821845]]\n",
      "============================\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# total training epoch, hyperparameter\n",
    "n_epoch = 400\n",
    "# number of data points, or whole batch size\n",
    "m = 100\n",
    "# simulated annealing parameter, hyperparameter\n",
    "t0, t1 = 5, 50\n",
    "# initialization of parameter vedtor \\theta\n",
    "theta = np.random.randn(2,1)\n",
    "# adding all zero power term(interception) to training dataset\n",
    "X_b = np.c_[np.ones((100,1)),X.reshape(100,1)]\n",
    "# store MSE\n",
    "mse_list = []\n",
    "# store theta\n",
    "theta_list = []\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "for epoch in range(n_epoch):\n",
    "    for i in range(m):\n",
    "        theta_list.append(theta)\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index,:]\n",
    "        yi = y[random_index,:]\n",
    "        grad = 2*xi.reshape(2,1).dot(xi.reshape(1,2).dot(theta)-yi)\n",
    "        mse = pow(xi.reshape(1,2).dot(theta) - yi, 2)\n",
    "        mse_list.append(mse)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * grad\n",
    "    if epoch % 40 == 0:\n",
    "        print(\"epoch %s: \"% epoch)\n",
    "        print(theta)\n",
    "        print(\"============================\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a448fab8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.07889703],\n",
       "       [3.75126053]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87d95969-5630-41a6-a38b-6cad9e251ef7",
   "metadata": {},
   "source": [
    "#### SGD MSE over iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "42d384bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(16,4))\n",
    "ax.plot(np.asarray(list(range(len(mse_list))))[::40], np.asarray(mse_list).flatten()[::40],label=\"mse_value\")\n",
    "ax.set_title(\"mse of SGD\")\n",
    "ax.legend(loc=\"upper right\")\n",
    "ax.grid(alpha=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e6168f1-95dc-48ea-8ed8-de5c18ac8222",
   "metadata": {},
   "source": [
    "#### SGD fitting line over iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "158507ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(6,4))\n",
    "ax.scatter(X, y, marker=\"*\", color=\"green\", s=4.5, label=\"raw\")\n",
    "iter_op = 1\n",
    "for index, (intercept, slope) in enumerate(theta_list):\n",
    "    if index == 0:\n",
    "        ax.plot(X, slope*X+intercept, lw=0.5,ls=\"--\",color=\"red\")\n",
    "    if index % iter_op == 0 and index != 0:\n",
    "        ax.plot(X, slope*X+intercept, lw=0.5,ls=\"-\",color=\"blue\")\n",
    "        iter_op *= 2\n",
    "ax.plot(X, theta[1]*X+theta[0], lw=1,ls=\"-\",color=\"magenta\", label=\"predict\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regressor fitting results\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\",rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bca6d86-ac30-47f5-b6d5-8325fd0189e0",
   "metadata": {},
   "source": [
    "#### SGD params searching route over iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "505b8b11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(6,4))\n",
    "theta_pts = np.asarray(theta_list).flatten().reshape(len(theta_list),2)\n",
    "ax.plot(theta_pts[:,1],theta_pts[:,0], lw=0.5, color=\"blue\",label=\"SGD\")\n",
    "ax.scatter(theta_pts[:,1],theta_pts[:,0], marker='.', lw=0.1, color='blue')\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"SGD searching routine\")\n",
    "ax.set_xlabel(r'$\\theta_1$')\n",
    "ax.set_ylabel(r'$\\theta_0$', rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c6b3216",
   "metadata": {},
   "source": [
    "# Polynomial Regression\n",
    "1. adding higher power terms by manipulating exsting data\n",
    "2. <font color=burgendy><b>sklearn.preprocessing PolynomialFeatures</b></font> could do, or simply numpy columnar manipulation would do\n",
    "\n",
    "original function be like:\n",
    "$$\n",
    "    0.5x^3 + 2.7x^2 + 3 + \\epsilon\n",
    "$$\n",
    "<center>* where $ \\epsilon \\sim \\mathcal N (0,1)$ </center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e7d99fe8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 30)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "%matplotlib inline\n",
    "\n",
    "# prepare input noise-added data\n",
    "m = 100\n",
    "X = np.sort(12*np.random.rand(m,1)-6, axis=0)\n",
    "y = 0.5 * X**3 + 2.7 * X**2 + 3 + 12 * np.random.randn(m,1)\n",
    "\n",
    "poly_features_3 = PolynomialFeatures(degree=3, include_bias=False)\n",
    "poly_features_30 = PolynomialFeatures(degree=30, include_bias=False)\n",
    "X_poly_3 = poly_features_3.fit_transform(X)\n",
    "X_poly_30 = poly_features_30.fit_transform(X)\n",
    "print(X_poly_30.shape)\n",
    "\n",
    "lin_reg_3 = LinearRegression()\n",
    "lin_reg_3.fit(X_poly_3,y)\n",
    "lin_reg_30 = LinearRegression()\n",
    "lin_reg_30.fit(X_poly_30,y)\n",
    "\n",
    "y_3 = lin_reg_3.intercept_ * np.ones_like(X) + X_poly_3.dot(lin_reg_3.coef_.T)\n",
    "y_30 = lin_reg_30.intercept_ * np.ones_like(X) + X_poly_30.dot(lin_reg_30.coef_.T)\n",
    "\n",
    "fig, ax = plt.subplots(1,1,facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray',figsize=(6,4))\n",
    "ax.scatter(X, y, marker='.', color=\"b\", lw=0.1)\n",
    "ax.plot(X, y_3, lw=0.5, ls=\"-\", color=\"red\", label=\"power-3 regression\")\n",
    "ax.plot(X, y_30, lw=0.5, ls=\"--\", color=\"green\", label=\"power-30 regression\")\n",
    "ax.legend(loc='upper left')\n",
    "ax.set_title(\"polynomial regression at different degrees\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"y\", rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "dad9db86",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.31244298] [[-0.74291301  2.89803208  0.55776375]]\n"
     ]
    }
   ],
   "source": [
    "print(lin_reg_3.intercept_, lin_reg_3.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb5ec0ea",
   "metadata": {},
   "source": [
    "# learning curve\n",
    "1. one efficient way to decide wether a model is over fitting or underfitting.\n",
    "2. main trick is increase volume of training set and testing set gradually and compare their cost function value, in regression case, this is MSE or RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f83acd98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's take cubic function above\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "    # list store mse of training and testing\n",
    "    train_errors, test_errors = [], []\n",
    "    # increase volume of training set gradually\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_pred = model.predict(X_train[:m])\n",
    "        y_test_pred = model.predict(X_test)\n",
    "        train_errors.append(mean_squared_error(y_train[:m],y_train_pred))\n",
    "        test_errors.append(mean_squared_error(y_test, y_test_pred))\n",
    "    plt.plot(np.sqrt(train_errors),lw=2,ls='-.', color='red', label=\" training set\")\n",
    "    plt.plot(np.sqrt(test_errors),lw=3,ls='-', color='blue', label=\" validation set\")\n",
    "    plt.legend(loc=\"upper right\")\n",
    "    plt.title(\"learning curve\")\n",
    "    plt.xlabel(\"Training set size\")\n",
    "    plt.ylabel(\"RMSE\", rotation=0)\n",
    "\n",
    "# this case we'll show underfitting\n",
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1029c7ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "polynomial_regression = Pipeline([\n",
    "    (\"poly_features\", PolynomialFeatures(degree=4, include_bias=False)),\n",
    "    (\"sgd_red\", LinearRegression())\n",
    "    ])\n",
    "plot_learning_curves(polynomial_regression, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eb46544",
   "metadata": {},
   "source": [
    "# Regularization\n",
    "1. basic concept is adding terms with regards to parameter vector on training cost function to constrain paramters\n",
    "2. usually cost function in training set is different from that in test set.\n",
    "3. lasso and elastic net tends to discard features that contribute less to label or target\n",
    "## Ridge Regression\n",
    "$$\n",
    "    J(\\theta) = MSE(\\theta) + \\alpha \\frac{1}{2}\\sum_{i=1}^{n}{{\\theta_{i}}^2}\n",
    "$$\n",
    "\n",
    "    > closed-form formula\n",
    "\n",
    "$$\n",
    "    \\hat \\theta = {(X^T \\cdot X + \\alpha I)}^{-1} + X^T \\cdot y\n",
    "$$\n",
    "* where $I$ is one $(n*n)$ identity matrix\n",
    "\n",
    "> linear_model Ridge or linear_model SGDRegressor(penalty='l2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8f4fd006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X_poly_30, y)\n",
    "y_pred_ridge = ridge_reg.predict(X_poly_30)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=0.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_pred_ridge, '-g', label=\"ridge regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdb5f3d4",
   "metadata": {},
   "source": [
    "## Lasso\n",
    "$$\n",
    "    J(\\theta) = MSE(\\theta) + \\alpha \\sum_{i=1}^{n}{|\\theta_{i}|}\n",
    "$$\n",
    "\n",
    "while this time subgradient formula is like:\n",
    "$$\n",
    "    g(\\theta,J) = \\nabla_{\\theta} MSE + \\alpha \\cdot sign(\\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f1e2d146",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "import warnings \n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "lasso_reg = Lasso(alpha=0.01)\n",
    "lasso_reg.fit(X_poly_30, y)\n",
    "y_pred_lasso = lasso_reg.predict(X_poly_30)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_pred_lasso, '-g', label=\"lasso regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f226f8e2",
   "metadata": {},
   "source": [
    "## Elastic Net\n",
    "$$\n",
    "    J(\\theta) = MSE + r\\alpha \\sum_{i=1}^{n}{|\\theta_i|} + \\frac{1-r}{2}\\alpha\\sum_{i=1}^{n}{{\\theta_i}^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6b47d871",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "# l1_ratio here is equal to r in formula\n",
    "elastic_net = ElasticNet(alpha=0.1,l1_ratio=0.5)\n",
    "elastic_net.fit(X_poly_30, y)\n",
    "y_pred_elanet = elastic_net.predict(X_poly_30)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_pred_elanet, '-g', label=\"elastic net regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7db06c2c",
   "metadata": {},
   "source": [
    "## early stopping\n",
    "stop training when rmse(cost function) reaches its minimum, which means we might reach global minimum\n",
    "\n",
    "<font color=purple><b>SGDRegressor parameters overview</b></font>\n",
    "\n",
    "    > loss='squared_error',\n",
    "    > penalty='l2',\n",
    "    > alpha=0.0001,\n",
    "    > l1_ratio=0.15,\n",
    "    > fit_intercept=True,\n",
    "    > max_iter=1000,\n",
    "    > tol=0.001,\n",
    "    > shuffle=True,\n",
    "    > verbose=0,\n",
    "    > epsilon=0.1,\n",
    "    > random_state=None,\n",
    "    > learning_rate='invscaling',\n",
    "    > eta0=0.01,\n",
    "    > power_t=0.25,\n",
    "    > early_stopping=False,\n",
    "    > validation_fraction=0.1,\n",
    "    > n_iter_no_change=5,\n",
    "    > warm_start=False,\n",
    "    > average=False,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5982f003",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1368\n",
      "[37.00324483] [ 5.31038599 27.49514751 19.09944076 11.20833209 11.85065701  1.21832872\n",
      "  6.00612423 -2.84684963  2.67939603 -4.09998668  0.92880318 -4.0470879\n",
      "  0.03506517 -3.39155054 -0.40761999 -2.47967061 -0.6133231  -1.48907127\n",
      " -0.69374726 -0.51309125 -0.70860432  0.39876113 -0.69189603  1.22061488\n",
      " -0.66491622  1.93989927 -0.64233793  2.55190155 -0.63490848  3.056775  ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.base import clone\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# for higher-power regression model, standardization is necessary\n",
    "std_scaler = StandardScaler()\n",
    "X_scaled_30 = std_scaler.fit_transform(X_poly_30)\n",
    "single_sgd_reg = SGDRegressor(max_iter=1, warm_start=True,  penalty=None,\n",
    "                              learning_rate=\"constant\", eta0=0.0005)\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "cnt = 0\n",
    "for epoch in range(20000):\n",
    "    single_sgd_reg.fit(X_scaled_30,y)\n",
    "    y_single_sgd_pred = single_sgd_reg.predict(X_scaled_30)\n",
    "    single_error = mean_squared_error(y_single_sgd_pred, y)\n",
    "    if single_error < minimum_val_error:\n",
    "        minimum_val_error = single_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(single_sgd_reg)\n",
    "        cnt = 0\n",
    "    else:\n",
    "        cnt += 1\n",
    "    # if mse doesn't increase in 20 consecutive epoch, \n",
    "    # assert convergence and leave iteration\n",
    "    if cnt >= 20:       \n",
    "        break\n",
    "\n",
    "print(best_epoch)\n",
    "print(single_sgd_reg.intercept_, single_sgd_reg.coef_)\n",
    "\n",
    "best_model.fit(X_scaled_30, y)\n",
    "y_single_pred = best_model.predict(X_scaled_30)\n",
    "fig, ax = plt.subplots(1,1, figsize=(6,4),\n",
    "                      facecolor='whitesmoke',\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(X,y, marker='.', color='b',lw=.5)\n",
    "ax.plot(X,y_30, '-r', label=\"linear regression\")\n",
    "ax.plot(X,y_single_pred, '-g', label=\"early stop strategy regression\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_title(\"regression result on power-3 polynomial function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b77bf670",
   "metadata": {},
   "source": [
    "# Logistic Regression\n",
    "1. commonly used to estimate the probability that an instance belongs to a particular class, all outputs of model will be processed through one continuously differentiable function.\n",
    "$$\n",
    "    \\sigma(t) = \\frac{1}{1 + e^{-t}}\n",
    "$$\n",
    "2. output of model will be precessed by\n",
    "$$\n",
    "    \\hat p = h_{\\theta}(x) = \\sigma(\\theta^T \\cdot \\vec x)\n",
    "$$\n",
    "3. for a sigmoid function, the threshold is always set as 0.5, this is used in one binary classifier\n",
    "4. cost function of logistic regression\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "    J(\\theta) & = & \\frac{1}{m}L(\\theta) \\\\\n",
    "    L(\\theta) & = & \\sum_{i=1}^{m}{y_{i}logp(x_i)} + \\sum_{i=1}^{m}{(1-y_{i})log(1-p(x_i))} \\\\\n",
    "    p(x_i) & = & \\sigma(\\theta^{T}x_{i}) \\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "5. derivitive form of cost function\n",
    "$$\n",
    "    \\frac{\\partial J(\\theta)}{\\partial \\theta_{j}} = \\frac{1}{m}[\\sigma(\\theta^{T}x) - y]x_j\n",
    "$$\n",
    "6. note that x here is a $(m,n)$ matrix where m stands for m features and n stands for n data points(entries)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cae9dc2d",
   "metadata": {},
   "source": [
    "## sigmoid function\n",
    "1. transfer $\\theta^T \\cdot x \\in R$ to $\\hat y \\in (0, 1)$ set\n",
    "2. also, sigmoid is a cdf function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f1714be2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "sigma_x = np.arange(-10,10,0.1)\n",
    "sigma_y = 1 /(1 + np.power(np.e, -sigma_x))\n",
    "fig, ax = plt.subplots(1,1,figsize=(12,4),facecolor='whitesmoke', edgecolor='gray')\n",
    "ax.plot(sigma_x, sigma_y, lw=1, ls= '-', color='blue',label=\"sigmoid core function\")\n",
    "fig.suptitle(\"function show\")\n",
    "ax.legend(loc=\"upper left\")\n",
    "ax.set_xlabel(\"t\")\n",
    "ax.set_ylabel(\"sigmoid\")\n",
    "ax.set_xticks(np.arange(-10,10.1,5))\n",
    "ax.set_yticks(np.arange(0,1.2,0.2))\n",
    "ax.set_xlim(-10,10)\n",
    "ax.set_ylim(-0.1,1.1)\n",
    "ax.set_title('sigmoid function show')\n",
    "ax.axhline(0, color='grey', linewidth=1)\n",
    "ax.axvline(0, color='grey', linewidth=1)\n",
    "ax.hlines(0.5,-12,12, ls=':', color='gray')\n",
    "ax.hlines(1.0,-12,12, ls=':', color='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "36ff43e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1}{1 + e^{- t}}$"
      ],
      "text/plain": [
       "   1   \n",
       "───────\n",
       "     -t\n",
       "1 + ℯ  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "init_printing(use_unicode=True)\n",
    "\n",
    "t = symbols(\"t\")\n",
    "ft = 1/(1 + exp(-t))\n",
    "ft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b83ca50d",
   "metadata": {},
   "source": [
    "## attribute of sigmoid function\n",
    "1. derivitives\n",
    "$$\n",
    "    \\sigma^{\\prime}(x) = \\sigma(x) \\cdot (1-\\sigma(x))\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "174fd098",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{e^{- t}}{\\left(1 + e^{- t}\\right)^{2}}$"
      ],
      "text/plain": [
       "    -t    \n",
       "   ℯ      \n",
       "──────────\n",
       "         2\n",
       "⎛     -t⎞ \n",
       "⎝1 + ℯ  ⎠ "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ft = diff(ft, t)\n",
    "df_ft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39ba8b03",
   "metadata": {},
   "source": [
    "## decision boundary\n",
    "1. take place where $\\sigma(\\theta \\cdot x) = 0.5$ . This time entries has equal probabiliy to be classified in either class\n",
    "2. for linear model in sklearn <font color=maroon><b>(LogisticRegression)</b></font>, <font color=maroon><b>predict()</b></font> will output its final class while <font color=maroon><b>predict_proba()</b></font> will output its original decision value, a number between 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "61d010d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename', 'data_module'])\n",
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
      "['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "raw_iris = load_iris()\n",
    "print(raw_iris.keys())\n",
    "print(raw_iris[\"feature_names\"])\n",
    "print(raw_iris[\"target_names\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "01a79774",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select oetal length feature\n",
    "X_iris = raw_iris.data[:,3].reshape(-1,1)\n",
    "# select virginica as target, make a binary classifier\n",
    "y_iris = (raw_iris[\"target\"] == 2).astype(np.int64)\n",
    "# initiate classifier\n",
    "logis_reg = LogisticRegression()\n",
    "logis_reg.fit(X_iris, y_iris)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c958c8bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iLvfdZ9a8J59eTiSnWa1Wjvz3VCkoKAiH5H1AJEf0/6U/O0J2UNOvJi82epEnaj1RoBPKuIQ49l3YZ0vIt53bxoGLBzBIXWdWyacSdQLqUDegLnUC6lAnoA6BnoF62CFSAKgmXUREsiQy0pwrPrHWPSEh5f62beG335Leh4SYI8uL5JTY2FjGjRsHwIgRI3BxcbFzRAVP7S9rs/fCXixYMDAo7FKYvnX7MqjBICr7VrZ3eHddZEwkm89uZt2pdaw/vZ6/zv3F9fjrqcqV9S5Lw5INaVSyEQ1KNqBuQF0Kuxa2Q8QicreoJl1ERO66woXhm2/M9WvXYPt22Lw5aWnYMKnshQtmTXuFCtCqVdJSurQdApcCw2KxUPq/L5lqH+0rsaY4MjaSz7Z9xidbP+GB8g8wuOFgHg56ON/Mp30x+iIbTm+wJeW7Qnel6kfu7epNw5INbUl5w5IN8ff0t1PEIpIbqSZdRESynWGYg9QlNndftQoeeih1bXti0t6vn9lEXiS7nQ4/zfF/j9s7jAKr7899OXH1RJr7HC2OJBgJlChcghcavEC/ev3w8/BLs2xuFX4jnDUn17Di+ApWnljJwUsHU5UpX6Q8zcs2p3mZ5jQr04wg3yAcLOp6IVLQZKYmXUm6iIjkiMhI2LgR1qwxl+3bk5L2mTPhv5myOHMGdu+G++8353QXuRPVP6+eZuIkuYuDxQEHiwM9qvfghYYv0LhU41zZ+iE2IZYtZ7ew4vgKVhxfwbZz20gwUj59rOlXk+ZlzKS8ednmlPIqZadoRSQ3UXN3ERHJdQoXNvupt21rvo+ISEraW7dOKvfTT+aAdM7O0LSpWT44GO65R6PHS+ZFxUbZOwTJAKthxWpYmXdgHj/s+4FafrUY0mhIrhho7tiVYyw9upQ/jv3B2pNriY6LTrG/sk9lHqzwIA9UeICWZVviW8jXTpGKSH6hmnQREclVPv8cPv449fRv/v5msj5unNm/XeR24uLi8H/fn3+t/9o7FMmk5APN9a/Xn/ceeA83J7ccuXZcQhwbz2xk6ZGl/Hr0Vw5dOpRif/FCxWlToQ1tKrThgfIPULZI2RyJS0TyNjV3vwUl6SIiuZ9hwD//wB9/mMvq1RAdDW5ucOkSeHiY5f76C0qWVNIuaYuNjaX4uOJEEGHvUOQOeLp4su9/++5qMvzv9X/59civ/Hr0V/745w/CY8Jt+5wcnGhWphntK7XnoYoPUcu/lvqUi0imqbm7iIjkaRYLVK5sLi+8ADExZtP4EyeSEnSA/v3h77/h3nvh0UfNpWZNNYsXk5OTEx6FPIi4piQ9L0kcUC7IN4gXG73IU7WfuivTkYVFhbH40GIWHlrIqhOriLfG2/YVK1SM9pXb06FyBx6q+BBF3Ipk+/VFRNKjJF1ERHI9V9eU/dbBnPbNw8NMyLdvN5c334SqVaFHD3jsMahWzT7xSu7g4OCAk5P+1MkrEmunO1XtxAsNX6Bl2ZbZPnjcmfAzLDy4kAUHF7Dh9Abb1HAAtfxq8WiVR+kQ1IEGJRrkm2nhRCTv0W8uERHJkwoVgk2bICwMliyBn3+G5cvh0CEYM8ZsLv/99/aOUuxtcMPBrD+93t5hFFhrTq4hMjYy3f0OFgeshpXihYrzfIPnGVB/ACUKZ2//lbCoMObtNwek23J2S4p9DUo0oGu1rnSp1oXKvpWz9boiIlmlPukiIpJvhIebCfu8eTBwIHToYG7fuxd69YInnjBfS5e2b5ySM6xWKyf+G4GwfPnyODioH3FOq/1lbfZe2Jtqu5ODE/HWeJqVbsaQRkPoVLUTzo7O2XbdiJgIFh9azPd7v2fF8RVYDStgDkjXrEwzulbrSudqnSnjXSbbrikicivqky4iIgWStzc8+aS5JDdvnpmojxgBI0eaTeeffhq6dNFc7PlZfHw83333HQAjRozAxcXFzhEVbBbMputuTm70qdOHQQ0GUcOvRradPzYhlt+O/sYP+37gl8O/cCP+hm1fo5KNeKLWE/So0YMAz4Bsu6aIyN2gJF1ERPK9l1+GcuVg9mxYuxZWrjSX55+Hrl1h/HgoXtzeUUp2s1gs+Pv729bFvir7Vr4rA8Htu7CP6bumM/vv2Vy6dsm2vYpvFXrV6sXjtR6nkk+lbLueiMjdpubuIiJSoJw8Cd99B99+C0ePgo8PnD9vDk4HcOOGOdWbiNy511e8zrF/jzGowaBsHQgu/EY4c/bNYfru6Ww7t822PdAzkCdqPcETtZ6gbkBdPZwRkVxD86TfgpJ0EREBcy72rVvNpP2xx5K2VasGlSqZfdrbtQMNDi6SOxiGwfrT6/lm5zfMPzCf6/HXAbN/+yNBj9Cvbj+CKwXj5KD/tCKS+6hPuoiIyG1YLNC4sbkk2rkTDh82l6VLoWRJ6NfPnI9dg82J2EdkTCSz/57NF399wf6L+23bqxWrRr+6/Xjqnqfw8/CzY4QiItlLNekiIiLJHDkCU6fCzJlw6b/urQ4O5kjx77wDdevaNTzJhLi4OL7/bx6+Xr164eycfaOHy9134OIBvvjrC77d861tGjcPZw8er/k4/er1o1HJRmrOLiJ5hmrSRUREsigoCD76CMaOhUWLYMoUWL3anNrtpZfsHZ1khmEYnDp1yrYuuV+8NZ6fD/3M5399zuqTq23bq/hW4fkGz9P7nt54u3nbMUIRkbtPSbqIiEgaXF3NvuqPPWY2f//pJ2jVKmn/2LEQHQ2DBkGpUnYLU27BycmJbt262dYl94qMieSbnd8waeskToefBsDB4kDHKh0Z1GAQD5R/QLXmIlJgqLm7iIhIJkVFmYl5eDg4OprTuA0bBg0a2DsykbzlbMRZPt36KVN2TCE8JhyA4oWK82y9Zxl470DKeJexc4QiItlDzd1FRETuInd3s8/6J5/AmjUwb565tG4Nr78ObdqYA9OJSNr2hO7h480f8+O+H4m3xgNQtVhVXmnyCk/WfhI3J82DKCIFl2rSRURE7sCePTBhAvzwA8SbuQbvvQcjRtg3LgGr1crZs2cBKFWqFA4ODnaOqGAzDIM1J9cwbsM4/jz+p217y7ItGXbfMNpXbo+DRf9GIpI/ZaYmXXdCERGRO3DPPTBrFhw7Bi++CF5e8PjjSftDQyEmxn7xFWTx8fHMmDGDGTNmEJ/4BEVynGEY/PHPHzSf0ZzW37bmz+N/4mBxoGeNnmzrv401fdbwcNDDStBFRP5j97vhlClTqF69Oj4+PjRt2pSNGzfesvycOXNo1KgRxYoVo0KFCgwcOJDLly/nULQiIiJpK1MGJk2CkBAoVy5p+//+BxUqwOTJcOOGvaIrmCwWCz4+Pvj4+GjQMTswDIMlh5fQeFpj2n7flo1nNuLi6MLz9z7PP4P/YU63OTQoqYEcRERuZtfm7vPnz6d///5MmjSJxo0bM23aNGbNmsWOHTsoXbp0qvKbNm0iODiYDz74gPbt23P+/HmGDBlCpUqVmDNnToauqebuIiKSU6KioEYNOG0OVk3JkjByJPTrZ44eL5IfWQ0riw4uYuz6sewO3Q2Au5M7A+sP5NWmr1KicAn7BigiYgd5prn75MmT6d27N3369KFq1ap89NFHlCpViqlTp6ZZftu2bZQtW5bnn3+ecuXKcd9999GvXz927tyZw5GLiIjcnqcnHD0KX31ljgZ/7pw5ZVvlyua22Fh7RyiSfQzD4OdDP3PPV/fQ7adu7A7djYezB6/d9xonh55kYtuJStBFRDLAbkl6bGwsu3bt4oEHHkixvXXr1mzdujXNYxo3bsy5c+f4/fffMQyDsLAwFi9eTNu2bdO9TkxMDBEREbYlMjIyWz+HiIjIrbi4wMCB8M8/8PnnUKIEnDljNoP/5ht7RyeSPVYeX0njaY3pNLcT+y7sw8vVizeav8Gpoaf44MEP8PPws3eIIiJ5ht2S9MuXL5OQkICfX8qbtr+/P2FhYWke07hxY6ZPn07v3r0pUqQIFSpUwNvbm48//jjd64wfP57AwEDbEhQUlK2fQ0REJCNcXeH5580B5j79FOrWhT59kvaHhoLVarfw8qX4+Hh++OEHfvjhBw0cd5dsObuFB759gDaz27Dt3DYKORdiZLORnHzxJO+2fhffQr72DlFEJM+x+8BxNw/kYhhGuoO7HDx4kGHDhvH666+zYcMGFi9ezMmTJxkyZEi65x82bBghISG25ciRI9kav4iISGa4ucHgwbBjBxQqZG5LSICHHoKGDWHVKvvGl59YrVaOHj3K0aNHseoJSLbaG7aXTnM60WRaE1adWIWLowtDGg7h+JDj/N8D/0dR96L2DlFEJM9ysteFfX19cXR0TFVrfuHChVS164nGjx9PkyZNeOmllwCoVasWHh4ePPjgg4wePZrAwMBUx7i6uuKq0XlERCSXSf48+sABOHHCHGjugQcgOBg++MCc3k2yztHRkUcffdS2LnfubMRZRq0axew9szEwcLA40Pue3rzV8i3KFilr7/BERPIFu9Wku7i4ULduXVbdVGWwevVqGjVqlOYx169fx8EhZcj6pSsiInldrVpmM/jBg8HJCf74w2wO/9RTcPKkvaPLuxwdHalTpw516tTR3wt3KCo2itGrRxM0OYhv93yLgUG36t3Y//x+pj86XQm6iEg2smtz98GDBzNz5kxmzZrFoUOHeO211zhz5gz9+/cHYPTo0bZ1gHbt2vHzzz8zdepUTpw4webNmxk2bBj33ntvmrXoIiIieYWfn9lX/dAh6NkTDAO++w6qVIG//7Z3dFJQJVgTmLZzGpUnV+bdde9yPf46zco0Y2v/rfzU/SeqFqtq7xBFRPIduzV3B+jWrRtXrlzh/fffJzQ0lOrVq7Nw4ULKlCkDQGhoKGfPnrWVf+qpp4iKiuLrr79mxIgReHt707JlS8aOHWuvjyAiIpKtKlaEOXNg2DAYPhxiYsyadsk8q9XKhQsXAPDz80vVGk9ubcXxFbyy/BX+DjOfElUoWoEP23xIl2pd0h0/SERE7pwlOjrasHcQOSkiIoLAwEDCw8NvO4m8iIiIPRkGREZC4q+riAh4/HEYNQruu8++seUFsbGxjBs3DoARI0bg4uJi54jyhqOXj/LSHy+x9OhSAIq4FeHNFm8yqMEgXJ00zo+ISFZERETg7e1NSEjIbfNQPVIWERHJpSyWpAQd4P33YdkyaNoUevWCZI3NJA0Wi4XChQtTuHBh1fxmQHRsNCNXjqTmlzVZenQpTg5ODGk4hH8G/8PLTV5Wgi4ikkNUky4iIpJHhIWZtejTp5u17IUKweuvw2uvmfOwi2SFYRgsOLiAl/94mTMRZwBoW6ktk4InUaVYFTtHJyKSP6gmXUREJB/y94dvvoHt26FZM7h2DUaPNvusr1hh7+gkLzp06RAPffcQ3X/qzpmIM5QrUo7FPRez7IllStBFROxESbqIiEgeU68erFsHP/wAgYFw9CjMmGHvqCQviYqNYvifw6n9ZW1WHF+Bq6Mro1uM5sDzB3i06qPqHiAiYkd2Hd1dREREssZiMQeRa98exo6FV15J2hceDp6eUNCnBo+Pj2fRokUAdO7cGScn/dkD8MvhXxi0bBBnI8xBDR4JeoSJwROp6FPRzpGJiAioJl1ERCRP8/aGjz6CgICkbX37QsOG8Ndf9osrN7BarRw4cIADBw5gtVrtHY7dnY88T7d53Xh0zqOcjThLhaIV+PXxX/nl8V+UoIuI5CJ6pCwiIpKPnDsHq1bB1avQqBEMGgTvvQeFC9s7spzn6OhIu3btbOsFldWwMmXHFIavGE5ETASOFkdeve9V3mz5JoWcC9k7PBERuYlGdxcREclnwsJg2DD47jvzfZky8PXX0LatfeOSnLf/wn4G/DqATWc2AdCwZEOmPjKV2v617RyZiEjBotHdRURECjB/f5g9G/78E8qXh9OnoV07ePpps4Zd8r8b8Td4c9Wb1P26LpvObMLTxZPJ7Sazqe8mJegiIrmcmruLiIjkU23awN698OabMGkSrF1bsAaTMwyDK1euAODj41NgRizfenYrz/z8DAcvHQSgY5WOfNbuM0p7l7ZzZCIikhFK0kVERPIxDw+YMAF69oSYmKS+6VYrXLxo1rrnV3FxcXz22WcAjBgxAhcXFztHdHfdiL/BW6vfYvzm8VgNKwGeAXzW7jO6VOtSYB5QiIjkB2ruLiIiUgA0agQtWiS9nzoVqlSBmTPByMej07i6uuLq6mrvMO66LWe3UPfruny46UOshpUnaz/J/uf307V6VyXoIiJ5jAaOExERKWAMA4KDzT7rAB07mgPLJZ/GTfKGG/E3GL16NB9v/thWe/71w1/TsUpHe4cmIiLJaOA4ERERSZfFAsuWwbhx4OwMv/wCNWvC/Pn2jkwyI7H2/KNNH2E1rDx9z9Psf36/EnQRkTxOSbqIiEgB5OQEr78O27fDPffA5cvQvTs88QT8N9aa5FKxCbGMWjmKptObcujSIQI9A/nlsV+Y1WkWPu4+9g5PRETukJJ0ERGRAqx2bdi2Dd54wxz5fe5cOHLE3lFlj/j4eBYvXszixYuJj4+3dzjZ4uDFgzSZ1oT3NryH1bDyVO2n2P/8fh6p8oi9QxMRkWyi0d1FREQKOBcXePddeOQRM2Fv3Dhpn2GYzePzIqvVyp49ewBo3769naO5M4Zh8Plfn/Pqn69yI/4GPu4+THl4Cl2rd7V3aCIiks2UpIuIiAgADRuaS6KDB+Hxx82R4Bs0sF9cWeXo6EibNm1s63nV+cjzPPPzMyw/thyA4IrBTH90OiUKl7BzZCIicjcoSRcREZE0DR8Oe/bAfffBmDHw2mtmk/i8wtHRkaZNm9o7jDsy/8B8Bv46kCvXr+Dm5MZHD37EoAaDNK2aiEg+pj7pIiIikqZZs8zB5OLjYeRIaN0aTp+2d1QFQ0RMBL0X96b7T925cv0K9QLrsXPATl5o+IISdBGRfE5JuoiIiKSpaFFzILkZM8DDA9atM0eCnzfP3pFljGEYREREEBERgWEY9g4nw7ad20adr+rw7Z5vcbA4MKr5KDb320y14tXsHZqIiOQAJekiIiKSLosF+vSB3bvN/upXr0LPnrBokZ0Dy4C4uDgmTpzIxIkTiYuLs3c4t2U1rHy08SOaTm/KiasnKOtdlnV91jG29VhcHF3sHZ6IiOQQ9UkXERGR26pUCTZsMPumr15tjgSfFzg45I36iLCoMHov7s0fx/4AoHv17kx5ZApF3IrYNzAREclxlujo6Ey3/5o9ezZdu3alUKFCdyOmuyoiIoLAwEDCw8Px8vKydzgiIiJ5Tnw8OP33mD82FubMgaeeyrtTtdnbn8f+5KlFTxEWHYa7kzuftP2E/vX6q++5iEg+EhERgbe3NyEhIbfNQ7P0ePmtt96iQoUK/O9//2PLli1ZClJERETyJqdk7fCGD4feveHRR+HyZfvFlBfFJcTx+orXeei7hwiLDqOmX022D9jOs/WfVYIuIlKAZSlJP3r0KNOmTePq1au0a9eOunXr8vHHHxMaGprd8YmIiEguVrkyuLjAkiVQty5s3GjviPKGE/+eoPmM5nyw8QMAnqv/HNv6b6N68ep2jkxEROwtS83dk7tw4QJz5szhu+++48iRIzz44IP07t2b9u3b58p+YGruLiIikr127TIHkzt61JxHfexYc051e/8ZEB8fzx9/mH28g4ODcXLKHUPxzNs/j2eXPEtETARF3IrwzSPf0LV6V3uHJSIid9Fdb+6enJ+fH02aNKFRo0Y4ODiwf/9+Bg4cSM2aNVm3bt2dnl5ERERyubp1YccOeOIJSEiAESOgfXu4cMG+cVmtVrZv38727duxWq32DQaIiY/hhWUv0HN+TyJiImhauim7B+5Wgi4iIilkOUkPCwtj0qRJ3HvvvbRt25aIiAjmz5/PgQMH+Oeff+jYsSMDBgzIzlhFREQklypcGL77Dr75BtzdYfNmiIy0b0yOjo60bNmSli1b4ujoaNdYTl49SfMZzfn8r88BGNFsBGv6rKFskbJ2jUtERHKfLDV379atGytWrKBSpUr06dOHJ554Ah8fnxRlQkJCqFy5MlFRUdkWbHZQc3cREZG7a98+OH3arE0XWHJ4CU8vfpqrN67i4+7D7M6zaV9ZPxwRkYIkM83ds9Q5q3jx4vzxxx80atQo3TIBAQEcOHAgK6cXERGRPKxmTXNJtHIlTJoEM2eCr6+9osp58dZ4Rq0cxYebPgSgUclGzOs+jzLeZewcmYiI5GZZau7erFkz6tSpk2p7bGws33//PQAWi4UyZW7/S2jKlClUr14dHx8fmjZtysbbDAsbExPD22+/TdWqVSlatCg1a9Zk1qxZWfkYIiIicpfFxUG/fvDrr1C/PmzfnnPXNgyDGzducOPGDQzjjsbJzbTzkedpPau1LUEf0nAI655ZpwRdRERuK0vN3QsXLsyxY8fw8/NLsf3y5cuUK1eOyAx2Qps/fz79+/dn0qRJNG7cmGnTpjFr1ix27NhB6dKl0zymR48eXLhwgdGjR1OxYkUuXrxIfHw8jRs3ztA11dxdREQkZ/39N3TtCv/8Y07X9umnMGAA3O2pwGNjYxk3bhwAI0aMwMXF5e5e8D+rTqzi8QWPcyH6AoVdCjP90el0q94tR64tUpBZrVZiY2PtHYYUYC4uLunOcHbXm7sbhoEljd+s586dw9vbO8PnmTx5Mr1796ZPnz4AfPTRR6xcuZKpU6cyZsyYVOWXL1/Ohg0b2Ldvn60PfNmyGnBFREQkN6td26xB79MHFi+G554z51P/6isoVMje0WUfq2HlvfXv8daat7AaVmr712Z+9/lU9q1s79BE8r3Y2FhOnDiRK2ZykILLwcGB8uXL3/FD4Uwl6U2aNMFisWCxWOjQoUOK+UYTEhI4deoUDz74YIbOFRsby65du3jllVdSbG/dujVbt25N85hly5ZRt25dJk6cyI8//oiHhwft27dn9OjRuLu7p3lMTEwMMTExtvcZreUXERGR7OPtDQsXwscfw+uvw+zZ5vzq69dDkSJ355rOzs688cYbAOnWbGSXK9ev0GthL37/53cA+tXtx+R2k3F3TvvvExHJPoZhEBISgqOjI6VLl77r/99F0mK1Wjl//jwhISGUKVMmzUrtjMpUkv7II48A8Pfff9OmTRs8PT1t+5ydnSlbtiydOnXK0LkuX75MQkJCqibz/v7+rFixIs1jTpw4webNm3Fzc2POnDlcunSJl156iX///ZevvvoqzWPGjx/Pe++9l6GYRERE5O6xWGDYMGjQAHr2NOdXz0QDvCxcz5IjU6/9HfY3ned25vi/x3F3cufLDl/Su07vu35dETHFx8dz7do1SpQoQaH81DxH8pzixYtz/vx54uPjcXZ2zvJ5MpWkjxw5EoAyZcrQrVs33NzcsnzhRDc/YUivKT2YTycsFgvTp0+3NauPiYmhV69eTJw4Mc3a9GHDhjF48GDb+8jISIKCgu44bhEREcmali3NWnRv76R+6ZGR4OYGd/A3jV3M3TeXvr/05VrcNcoXKc+inou4J+Aee4clUqAkJCQA5Ni4EyLpSfwOJiQk5FySnujJJ5/M8gUT+fr64ujoSFhYWIrtFy5cSFW7niggIIASJUqk6PdepUoVDMPg3LlzVKpUKdUxrq6uuLq63nG8IiIikn0CA5PWrVZ44gm4ehV++gkCArLnGgkJCaxcuRKABx54IFtr1ROsCYxYOYKPNn0EwEMVH+LHrj/i4+6TbdcQkcy5k+bFItkhu76DGe6wUapUKS5dugRAyZIlKVWqVLpLRri4uFC3bl1WrVqVYvvq1avTnX+9SZMmhISEEBUVZdv2zz//4ODgQMmSJTP6UURERCQXOXIE1q2DDRvMadq2bMme8yYkJLB582Y2b95sq2nLDpevXabd9+1sCfrwpsNZ9sQyJegiIpItMlyT/v7771O4cGHbenY8JRg8eDD9+/enbt26NGrUiOnTp3PmzBn69+8PwOjRozl//jzffPMNYE6/9v777/Pcc88xatQoLl++zKhRo3j66afTHThOREREcreqVWHbNujcGQ4ehBYt4LPPzGna7oSjoyNNmjSxrWeHPaF76Dy3MyeunqCQcyFmPDqDHjV6ZMu5RUTSYrFYWLRoUYbH/sqsVq1aUadOHSZNmnRH53n77bdZvHgxu3fvzvAx5cqVY+jQoQwdOvSOrp3fZGme9Ow0ZcoUJk6cSGhoKNWrV+eDDz6gWbNmAAwYMIDTp0/z+++/28ofPnyYV155hS1btuDj40OXLl146623Mpyka550ERGR3Cky0pymbeFC833//maynlt6rc3ZN4e+P/flevx1KhStwOKei6nlX8veYYkUeDdu3ODEiROUL18+W8bMykl9+vTh6tWrLF68ON0yoaGhFC1aNFNdeGNjYylRogRDhw61zXKR3Lhx4/j44485f/48UVFRODs72ypksyoqKoqYmBh8fX0zfMzFixfx8PDINwP+3eq7mJl50jOcpEdERGQ4uNyc/CpJFxERyb0MA95/H0aNMte7doX58+0bU7w1nhErRjB+83gAgisG80PXH9S8XSSXyK9Jemxs7B0Nhjd06FB+/fVXjh49mqoVdFBQEB06dGDixIm3Pc+dxlGQZFeSnuE+6SVKlKBkyZK3XBLLiIiIiGSFxQIjRsCyZebgcsOHZ/1chmGQkJBAQkIChpG1hoOJ/c8TE/QRzUaw9ImlStBFJNu1atWKF154gZdffplixYrx4IMPAmZz98QkPjY2lhdeeIHAwEDc3NwoV64c48aNS/N8/fr149ixY6xbty7F9vXr13P06FH69etnu27y5ublypVj7Nix9OnTB29vb5599lkApk6dSunSpSlUqBCdO3dmwoQJFClSxHbc22+/TZ06dWzv+/TpQ6dOnRg/fjyBgYH4+voyaNAg4uLiUlwreTP7q1evMmDAAPz9/XFzc6NmzZr8+uuvgDmF9+OPP06pUqUoVKgQtWrV4scff8zUzzivyHCf9N9+++1uxiEiIiJi07YtHD9uTsuW6OBBs/96RofFiYuLs/3xOmLEiEzXBO0O3U3nuZ05efUkHs4ezOw0k27Vu2XqHCKS8wzD4FrcNbtcu5BzoTsau2vWrFn873//Y+PGjWk+XPz000/55ZdfmDdvHmXKlOHMmTOcOXMmzXPVqlWLBg0aMGPGDFq2bGnbPn36dBo2bEjNmjXTjeOjjz7izTfftDWV37hxI8899xwffPABHTt2ZMWKFbz55pu3/TyrV68mMDCQ1atX888//9CzZ0/q1KljS/yTs1qttGvXjsjISL777jsqVqzIgQMHbGOK3Lhxg/r16zN8+HC8vLxYunQpTz31FBUqVEh34PG8KsNJevPmze9mHCIiIiIpJE/Qd+6E++6DHj3gq6/gbndf/HHvj/T7pR/X469TsWhFFj+2mJp+6f9BKyK5x7W4a3iO87TLtaNGROHh4pHl4ytVqsSHH36Y7v7Tp09TuXJlmjVrhsVioWzZsrc8X9++fRk2bBifffYZnp6eREVF8dNPPzFhwoRbHte6dWuGDRtme//GG2/Qrl0727agoCA2bdpkq+VOT9GiRfnss89wdHSkatWqdOjQgZUrV6aZpK9YsYJt27Zx8OBBgoKCAKhQoYJtf8mSJVPENHjwYH7//Xd++umnfJekZ7i5+969e7Farbb1Wy0iIiIi2WnPHoiPh9mzoVkzOHny9sc4OzszfPhwhg8fjrOzc4auE2+NZ9jyYTyx8Amux1+nbaW2/PXsX0rQRSRH3Hvvvbfc36dPH3bv3k2VKlUYMmQIy5cvt+177rnn8PT0tC0Ajz/+OFarlblz5wIwd+5cDMPgsccey1Qchw8fpmHDhim23fw+LTVq1Egxu0ZgYCAXLlxIs+zu3bspVaqULUG/WUJCAv/3f/9H7dq18fX1xdPTk+XLl3P69OnbxpHXZLgmvUmTJhw/fhw/Pz+aNGmCxWJJswmGxWIhMjIyW4MUERGRgu2ZZ6B8ebMmfdcuuPdemDMH2rRJ/xiLxZKpQaQuXbvEY/MfY+WJlYDZ//zd+9/F0SF7pm8TkZxRyLkQUSOi7HbtO+Hhceta+Hr16nHixAl+++03VqxYQY8ePWjTpg3z589nzJgxKWqaAby9venWrRszZsygX79+zJgxg27dut124LKb4zAMI1Uz/oyM9XHzA1KLxWKr+L3Z7Wbr+vjjj5k4cSKTJk2iVq1aeHh4MHToUGJjY28bR16T4ST9wIEDFC9e3LYuIiIikpNatYIdO6BLF9i+HYKDYdw4ePXVjPdTT8+ukF10ntuZU+Gn1P9cJI+zWCx31OQ8t/Py8qJnz5707NmTbt260bZtW65cuYKfnx9+fn6pyvfr149WrVrx66+/snHjRt57771MX7Nq1aps27Ytxbbt27dn+TOkpXbt2pw9e5YjR46kWZu+fv16Hn30UZ588knA7MN+9OhRqlWrlq1x5AYZTtLLlCmT5rqIiIhITildGtavh0GDYPp0c/T3MmUgrZabCQkJrF+/HjDH1kne5DK5H/b+QP9f+nM9/jqVfCqxuOdiavjVuJsfQ0QkSyZOnEhgYCB16tTBwcGBn376iYCAgBSjrN+sZcuWVKpUiaeffppKlSrRokWLTF938ODBtGjRggkTJvDII4+watUqfvvttzsaJC+tOFu0aEHXrl2ZMGEClSpV4tChQ1gsFtq2bUulSpVYsGABmzZtomjRokyYMIHQ0NB8maRnuE/6zY4cOcLLL79M+/bt6dChAy+//DJHjhzJzthEREREUnFzg2++gc8/h06doHv3tMslJCSwdu1a1q5dS0JCQqr98dZ4Xv7jZXot7MX1+Ou0q9SObf23KUEXkVzL09OTDz74gHvvvZcGDRpw8uRJli1bhoPDrdO6vn378u+//9K3b98sXbdp06Z89dVXTJgwgXvuuYfff/+dl156KdvnpV+wYAENGjTg8ccfp3r16rz22mu2+/ebb75JvXr1CA4OplWrVgQEBNCpU6dsvX5uYYmOjs70xKGLFi2iT58+1KtXzzZgwF9//cWOHTuYMWMGXbp0yfZAs0tERASBgYGEh4ffti+GiIiI5G6GkdTU/cYNsxl8s2bm+/j4eP744w8AgoODcXJKakB4Mfoijy14jFUnVgEwqvko3mn1jvqfi+RBN27c4MSJE5QvXz7bk0ZJ37PPPsuhQ4dsLZbk1t/FiIgIvL29CQkJuW0emuHm7sm98cYbDBs2LNXceGPHjuXNN9/M1Um6iIiI5B+JCbphwHPPmaO/J/ZTd3JyokOHDqmO2Rmyk85zO3M6/DQezh582/lbulTT3y4iIrcyfvx4HnzwQTw8PPjtt9+YNWsWX3zxhb3Dypey1Nw9LCyMJ554ItX2xx57jLCwsDsOSkRERCQzEhLAyQmsVrOf+mOPQXR06nLf/f0dTac35XT4aSr7VGZr/61K0EVEMmDbtm08+OCD1KpVi6+++opPP/2U/v372zusfClLNenNmzdn48aNVKxYMcX2TZs2cd9992VLYCIiIiIZ5eQEU6eaU7MNGQLz5sHBg7BoEVSsaPY/f3X5q0zaOgmA9pXb832X7yniVsSucYuI5BXz5s2zdwgFRoaT9KVLl9rWO3TowJtvvsnu3btp0KABYPZJX7hwIW+88Ub2RykiIiJyGxaL2eS9Vi3o2hUOHYpl1qwPcHSEdWXWsOq02f/8zRZv8nart3GwZHn8XBERkbsmwwPHeXp6ZuyEFguRkZF3FNTdpIHjRERE8r9z56Bnz1gefHAcAP8XMwnXwvF82+lbOlfrbOfoRCQ7aeA4yS1yfOC4qKiorEUqIiIiksNKloRnJsxj2Cv+JFRaQvl6fix6bBHVi1e3d2giIiK3lKU+6SIiIiK5VVxCHMOWD+PTbZ9CG3g46GG+67wNbzdvVq+G0qWhUiV7RykiIpK2LCfp0dHRrF+/nrNnzxIbG5ti3/PPP3/HgYmIiIhk1oXoC/T4qQdrT60FYHSL0bzV6i0cLA4cPQqdO5t913/8Edq2tXOwIiIiachSkr579266dOnC9evXiY6OpmjRoly+fJlChQpRvHhxJekiIiKS47af306XuV04E3GGwi6FmdlxJv5X/dm8aTONGzfGw8ORatVgyxZo3x7+7//g9deT5loXERHJDbI0rOnrr79O+/btOXv2LO7u7qxZs4ZDhw5Rt25d3nvvveyOUUREROSWvt3zLc2mN+NMxBmCfIPY2n8rD1d+mBUrVrBixQoSEhIoUQLWrIEBA8AwYORI6N4dNOyOiEiSNWvWYLFYuHr16l27hsViYfHixXd8nlatWjF06NAMlz958iQWi4Xdu3ff8bXvpiwl6X///TdDhgzB0dERR0dHYmJiKFWqFGPHjuXtt9/O5hBFRERE0haXEMeQ34bQe3FvYhJieCToEbb130a14tVwcHDgnnvu4Z577sHBwfyTx9UVvv7aXJydYcECaNwY/vnHzh9ERAqcPn36YLFYeP/991NsX7x4MZZMNvEpV64ckyZNypZy9913HyEhIXh7e2cqhh07dmCxWNiwYUOa+4ODg+nYsSMAISEhtGvXLlPnT8vChQt59913M1y+dOnShISEULNmzTu+9t2UpSTd2dnZ9sXx8/PjzJkzAHh5ednWRURERO6mC9EXaDO7DZO3TQbgrZZvsfixxXi7mX9YOjk50alTJzp16oSTU8oefgMGwNq1EBgI+/fDF1/kePgiIri5ufHBBx/w77//2jsUAOLi4nBxcSEgICDTDwrq16/PPffcw4wZM1LtO3PmDCtWrKBfv34ABAQE4Orqess4MsLHx4fChQtnOEZHR0cCAgJS/U7IbbKUpNeuXZudO3cC0KJFC8aOHcucOXN47bXXqFGjRrYGKCIiInKzv879Rf0p9Vl3ah2FXQrz82M/83art3GwZPxPmyZNYMcOeOEFuKkiS0QkR7Rp04aAgADGjRt3y3ILFiygRo0auLq6Uq5cOT7++GPbvlatWnHq1CleeuklLBZLppJri8XCV199xaOPPoqHhwdjx45N1dz91KlTPPLIIxQtWhQPDw9q1KjBsmXL0jxfv379mDdvHtHR0Sm2z5w5k+LFi9OhQwfbdRObuyc2QZ83bx6tWrXCzc2N7777jvj4eIYMGUKRIkXw9fVl+PDh9O7dm06dOqX47Mmbu5crV4733nuPvn37UrhwYcqUKcOUKVNs+9Nq7r5//346dOiAl5cXhQsXpnnz5hw7dgyAv/76iwcffJBixYrh7e1Ny5YtbXnw3ZSlJP2dd94hICAAgDfffBMfHx+GDh3KxYsXmTx5crYGKCIiIpLc9F3TaT6jOWcjzlLFtwrbnt1Gxyods3SuwECYPBlcXMz38fEwdixERmZjwCJiF9HR6S83bmS87PXrGSubFY6Ojrz33ntMnjyZs2fPpllmx44d9OjRg8cee4y9e/fy9ttv8+abbzJz5kzAbPJdqlQpxowZQ0hICCEhIZmK4a233uLRRx9l79699O3bN9X+QYMGERMTw7p169i7dy8ffPABnp6eaZ6rV69exMXF8dNPP9m2GYbBzJkz6d279y1rsIcPH86QIUM4ePAgwcHBfPDBB3z//ffMmDGDjRs3EhERkaF+7B9//DH33nsvu3bt4vnnn+d///sfhw4dSrPsuXPnaNGiBW5ubqxatYodO3bQt29f4uPjAYiMjKR3796sX7+eLVu2ULlyZdq3b0/kXf4lkaV6/nr16tnWixcvzqJFi7ItIBEREZG0xCbEMvT3oXy5/UsAHq3yKLM6zbI1b09VPjaWCRMmAPDyyy/jkpiJ38Ibb8AHH5hTtC1eDJUrZ1v4IpLD0skjAXOGh6VLk977+cG1a2mXbdnSHHQyUblycOlS6nKGkZUooXPnztSpU4e33nqLadOmpdo/YcIEHnjgAd58800AgoKCOHDgAB999BF9+vTBx8cHR0dHChcubKtIzYwnnngiRXJ+4sSJFPtPnz5N165dqVWrFgAVKlRI91w+Pj506tSJGTNm0KdPH8AciO748eNpPgBIbujQoXTp0sX2fvLkyYwYMYLOnTsD8Nlnn6Vbg59c+/btbbONDR8+nIkTJ7JmzRqqVq2aquznn3+Ot7c3c+bMwdnZGTB/volat26dovzXX39N0aJFWbt2LQ8//PBtY8mqLNWkJ7pw4QIbN25k06ZNXLx4MbtiEhEREUnhfOR57p91P19u/xILFt69/10W9lyYboKeKCYmhpiYmAxfp1Mns3b9wAFo0CDlH/EiInfLBx98wKxZszhw4ECqfQcPHqRp06YptjVt2pSjR4+SkJBwx9e+9957b7l/yJAhjB07lqZNm/LWW2/x999/2/bVqFEDT09PPD09bQPB9evXj3Xr1vHPfyNyTp8+naZNm1KlSpUMxxEeHk5YWBgNGza0bXN0dKR+/fq3/Ty1a9e2rVssFgICArhw4UKaZXfv3k3z5s1tCfrNLly4wHPPPUdQUBDe3t54e3sTFRXF6dOnbxvHnchSTXpERAQvvfQS8+fPt30xHB0d6dq1KxMnTsz0SIAiIiIi6dl4eiPdfupGaFQo3q7e/ND1B9pXbn/b45ydnXnhhRds6xnRuLHZT717d9i4ER55BMaMMadrc7ijqg0RyWm3ml7R0THl+3RyOCD1//2TJ7McUrpatGhBcHAwI0eOtNVAJzIMI1U/cyOr1fZp8PDwuOX+/v37ExwczNKlS1m+fDnjxo3j448/ZvDgwSxbtsw2yJu7uztg9rMvW7YsM2fO5LXXXmPhwoV89tlnWYojK5/75vu9xWLBarWmWTYx5vT06dOHixcvMmnSJMqWLYurqytNmjQhNjb2tnHciSz9uhk0aBDbt29n/vz5nD9/npCQEObPn8+uXbtsvwxFRERE7oRhGHzx1xfcP+t+QqNCqelXk+0DtmcoQQfzDzNfX198fX0zNZBSYCCsWgX/+5/ZfPXNN6FrV/VTF8lrPDzSX9zcMl725jwuvXJ36v3332fJkiVs2rQpxfbq1aunmtZs06ZNBAUF4fjf0wYXF5dsqVVPT+nSpXnuuedYuHAhr7zyClOnTgWgbNmyVKpUiUqVKlGyZEnAvPc+88wzzJo1ix9++AEHBwd69OiRqet5e3vj7+/Ptm3bbNsSEhLYtWtX9n0ozFr39evXpzua/Pr16xkyZAjt27e3Ddx3Ka2+DtksS0n677//zpdffsmDDz5oGwXvwQcf5LPPPuP333/P7hhFRESkgLkRf4N+v/Rj0LJBxFnj6FGjB5v7baaST6Ucub6Lizkt2zffmOvLl8OpUzlyaREpoGrVqkWvXr1SDcT9yiuvsHLlSt59912OHDnCrFmz+Oyzzxg2bJitTLly5Vi3bh3nzp3L9iRy6NCh/PHHH5w4cYKdO3eyatUqqlWrdstjnnnmGc6fP8/IkSN57LHHbltbn5bBgwczbtw4fv75Zw4fPsyLL77Iv//+m+mp4W7lhRdeICIigscee4zt27dz9OhRZs+ezeHDhwGoVKkSs2fP5uDBg2zdupVevXrdtvY9O2QpSffx8cHLyyvVdi8vL4oUKXKnMYmIiEgBdib8DM1nNGfG7hk4WBz4sM2HzOk6B0+XW4wClYaEhAS2bdvGtm3bslzD1K8frFsH338PNWtm6RQiIhn27rvvpmrSXa9ePebNm8ecOXOoWbMmo0ePZsyYMSmaxY8ZM4aTJ09SsWJFihcvnq0xJSQkMGjQIKpVq0bbtm2pUqUKX3zxxS2PKVOmDG3atOHff/+97YBx6Rk+fDiPP/44Tz/9NE2aNMHT05Pg4GDcbm4GcQd8fX1ZtWoVUVFRtGzZkvr16zN16lRbk/np06fz77//UrduXZ566imGDBmCn59ftl0/PZbo6OhMd2iYPn06CxcuZOrUqQQGBgIQGhrKgAEDePTRR22T1OdGERERBAYGEh4enuaDBhEREbGfNSfX0OOnHly8dhEfdx/mdptLmwptsnSu2NhY29zDI0aMyNDo7hmxaZPZHF791EVyhxs3bnDixAnKly+frQmc5C5Wq5Vq1arRo0cP3n33XXuHk6ZbfRcjIiLw9vYmJCTktnlohgeOa9KkSYqmBceOHaNatWqULl0agDNnztja6OfmJF1ERERyH8MwmLRlEq/++SoJRgJ1A+qysOdCyhUpl+VzOjg4UL16ddt6doiIgG7dICQEtm+Hb78FPfMXEcl+p06dYvny5bRs2ZKYmBg+++wzTpw4wRNPPGHv0O66DCfpjzzyyF0JYMqUKUyaNInQ0FCqVavGhx9+mGqKgbRs3ryZ4OBgqlevzpYtW+5KbCIiInL3RcdGM+DXAfyw9wcAnqr9FF8//DXuznfW78/JyYnu3btnR4g2Xl7wf/8Hzz0HP/8MjRqZ86nfZmYhERHJJAcHB2bOnMmwYcMwDIOaNWuyYsWK2/aHzw+y1Nw9u8yfP5/+/fszadIkGjduzLRp05g1axY7duyw1dCnJTw8nKZNm1KhQgUuXLiQqSRdzd1FRERyj8OXDtN1Xlf2X9yPo8WRicETeaHhC9k6MNDdsG0bdOkC586Zifvs2dCxo72jEimY1Nxdcovsau5+R22/du3axY8//sicOXPYvXt3po+fPHkyvXv3pk+fPlStWpWPPvqIUqVK2Yb0T8+QIUPo0aMHjRo1ymLkIiIiYm/zD8ynwdQG7L+4nwDPAFb1XsXgRoNzfYIO0LChOZ968+ZmE/hHH4V33oF0puIVERHJsCwl6RcuXKBdu3Y0b96cV199lVdeeYVmzZrRvn17Ll68mKFzxMbGsmvXLh544IEU21u3bs3WrVvTPe7bb7/l+PHjjBw5MkPXiYmJISIiwrZEapJTERERu4pLiOPlP16m+0/diYyNpEXZFuwauIsWZVtk73Xi4pgwYQITJkxIdw7cO+HvDytWwAsvmO/37YM88HxBJN+6eVR0kZyWXd/BLCXpw4YNIzIyku3bt3P27FnOnTvHX3/9RWRkZIr5+m7l8uXLJCQkpBrC3t/fn7CwsDSP+eeffxg9ejTTp0/HySlj3enHjx9PYGCgbQkKCsrQcSIiIpL9zkWc4/5Z9zNxy0QAXrvvNVY+vZIAz4Bsv5ZhGERGRhIZGXnX/nh3cYHJk2HePJgxIylJV64gknMcHR0BsxJQxJ4Sv4OJ38msyvDAccn9+eef/Prrr1StWtW2rVq1akycOJGOmeyQdXOTNsMw0mzmlpCQwDPPPMMbb7xB5cqVM3z+YcOGMXjwYNv7yMhIJeoiIiJ2sPrEah5b8BgXoi/g5erFrE6z6FS10127npOTEwMHDrSt303Jx6czDHjqKWja1BxgTrXrIneXk5MThQoV4uLFizg7O2fbbA4imWG1Wrl48SKFChW64985WTraarWmeWEnJyesGeyM5evri6OjY6pa8wsXLqQ5QXxkZCQ7d+5kz549vPzyy7Y4DMPAy8uLX375hVatWqU6ztXVFVdX1wzFJCIiItnPalj5cOOHjFo1CqthpbZ/bRb0WEAln0p39boODg4EBGR/Df3t/PILfP+9uWzYAF9/DZ6eOR6GSIFhsVgIDAzkxIkTnDp1yt7hSAHm4OBAmTJl7nhslSwl6S1btuS1115j5syZBAYGAnD+/Hlef/31NBPltLi4uFC3bl1WrVqVovZ99erVdOjQIVV5Ly8vtm3blmLb1KlTWbt2Ld999x3lypXLykcRERGRu+jf6//Se3FvlhxZAkCfOn34vP3nFHIuZOfI7p6OHeGjj+D11+GHH2DnTpg/H2rUsHdkIvmXi4sLlStXVpN3sSsXF5dsacmRpSR9woQJ9OjRg2rVqlGqVCksFgtnzpyhRo0aTJs2LcPnGTx4MP3796du3bo0atSI6dOnc+bMGfr37w/A6NGjOX/+PN988w0ODg7UuOm3W/HixXF1dU21XUREROxvx/kd9Jjfg+P/HsfV0ZXP2n9Gv7r9cmz09oSEBPbu3QtArVq17riPYEZZLDBsGDRuDD17wqFD5mjwX31lNoMXkbvDwcFBU7BJvpClJL1UqVJs2rSJlStXcuTIEQzDoGrVqrRu3TpT5+nWrRtXrlzh/fffJzQ0lOrVq7Nw4ULKlCkDQGhoKGfPns1KiCIiImInhmEwedtkhi0fRpw1jnJFyrGgxwLqBdbL0TgSEhL4+eefAahevXqOJemJmjWDXbugVy9zFPinn4bDh2Hs2BwNQ0RE8hhLdHR0psYfjY+Px8fHh82bN+fJGuyIiAgCAwMJDw+/7STyIiIikjn/Xv+Xvr/0ZfGhxQB0qtqJ6R2nU9S9aI7HEh8fz7x58wDo0aPHXR88Lj0JCWZi/t57sGqVOaCciIgULBEREXh7exMSEnLbPDTTv62cnJwoU6YMCQkJWQ5QRERE8p8tZ7fw2PzHOBV+ChdHF8Y/OJ4XGr6QY83bb+bk5MQTTzxhl2sn5+gIb70F/fpBqVJJ20+eBA2pIyIiN8tSr/bXXnuNt956iytXrmR3PCIiIpLHWA0rH238iOYzmnMq/BQVi1ZkU99NDG402G4Jem6UPEE/cACqVzcT9+ho+8UkIiK5T5bafX355ZccP36cSpUqUaZMGQoVSjlC66ZNm7IlOBEREcndLl27RO/FvVl2dBkAPWv0ZMojU/ByVZeyW1m3Dm7cgOnTYdMmmDsXate2d1QiIpIbZClJf+SRR7BYLBhGprqzi4iISD6y7tQ6Hl/wOOcjz+Pm5ManbT+lf73+uab2PC4ujq+++gqA5557DmdnZztHlOS55yAoCJ58Mmn09wkT4H//M0eHFxGRgitTSfq1a9cYNWoUS5YsIS4ujlatWvHxxx9TrFixuxWfiIiI5DLx1njeW/8e76x9B6thpWqxqszrNo9a/rXsHVoKhmHYuublxoqF1q1hzx7o0weWLYNBg8xR4L/5Bnx87B2diIjYS6b6pI8dO5bvvvuOtm3b0r17d9asWcPQoUPvUmgiIiKS25z49wQtZ7bkrTVvYTWs9L6nN9uf3Z7rEnQwB4575plneOaZZ+w2svvtFC8Ov/5q1qI7O8OiRTBtmr2jEhERe8rUFGw1a9bkrbfeonv37gBs376dBx54gCtXruT43KNZpSnYREREsub7v7/n+WXPExETgZerF1+0/4JetXvZO6x8Y8cOmDzZrEnPpc8UREQkizIzBVumatLPnj1L02STe9577704OTkREhKStUhFREQk1wu/EU6vhb14ctGTRMRE0LR0U3YP3K0EPZvVrw8zZyYl6DduQP/+cOKEXcMSEZEclqkkPSEhIdWgK05OTsTHx2drUCIiIpI7bDi9gXu+uocf9v6Ao8WRMa3GsKbPGsoXLW/v0G7LarWyf/9+9u/fj9VqtXc4mfbOO2bT99q1YcYMyIXd6kVE5C7IVGMqwzAYOHAgrq6utm03btxgyJAheHh42Lb9+OOP2RehiIiI5Li4hDjGrB3Dexvew2pYqVC0At93+Z7GpRrbO7QMi4+PZ/78+QCMGDECFxcXO0eUOQMHwoYN5tK3LyxZAlOmgMbrFRHJ3zKVpPfqlbpZ22OPPZZtwYiIiIj9Hbl8hKcXPc3Wc1sB6H1Pbz5t92mem/vcYrFQtmxZ23peU64crFkDH30Eo0ebg8pt2mTOrd6+vb2jExGRuyVTA8flBxo4TkREJG1Ww8pn2z7j9RWvcz3+Ot6u3nz98Nf0rNnT3qEVeLt2Qa9ecPCg+f7TT2HwYPvGJCIiGXfXBo4TERGR/Onk1ZM88O0DvPj7i1yPv06bCm3Y+7+9StBzibp1zdHfhwwBb2/o2NHeEYmIyN2iJF1ERKQAMwyDb3Z+Q60va7Hm5BoKORfii/ZfsPzJ5ZT2Lm3v8CQZd3f45BM4ehT+a8UPmM3gY2LsF5eIiGQvzcIpIiJSQJ2PPM+zS55l2dFlADQt3ZSZnWZSyaeSnSPLHnFxcUybNg2Afv36pZqhJq8qXjxpffly6NIFatQwp2+79167hSUiItlENekiIiIFjGEYfP/399T8oibLji7DxdGFjx78iLV91uabBB3MzxkWFkZYWBhGPp2/LCEB/Pxg/35o3BhGjlStuohIXqeB40RERAqQM+FneG7pc7ba83qB9fi207fU8Kth58iyn9Vq5cSJEwCUL18eB4f8WTdx6ZLZVz1xBtzq1c151Rs2tG9cIiKSRAPHiYiISApWw8qXf31JjS9q2GrP373/Xbb025IvE3QABwcHKlasSMWKFfNtgg7mvOk//AALF4K/Pxw4AE2awPvv2zsyERHJivz7G0tEREQAOHzpMK1mtuL5Zc8TGRvJfaXvY/fA3bzR4g2cHfNHP22Bzp3NZu9PPAFWK1SsaO+IREQkK5Ski4iI5FNxCXG8v+F97vnqHtafXo+HsweT201m/TPrqVa8mr3Du+usVitHjhzhyJEjWK1We4eTI3x94fvvYfNm6N49afumTXDliv3iEhGRjFOSLiIikg9tP7+dRt80YsTKEcQkxBBcMZj9z+/nhYYv4GApGL/+4+Pj+fHHH/nxxx+Jj4/HYrGkWJydnSlWrBi1atWiT58+LFiwgPj4eLvFW65cOSwWS5aPP3nyJBaLhVatWtG4cdL2S5fg0UehWjWz37o9xtBr1apVqp+/o6MjxYoVIzg4mF9++SXng7qLkv9biIhklqZgExERyUeu3rjKqJWj+HL7lxgY+Lj7MDF4Ik/VfuqOEsC8yGKxUKJECdt6ot69ewNmTXt4eDhHjhzh22+/ZdasWVSqVInvv/+ehvlo1LULF8wR4A8cMJvCf/stfPEFlC+f87EEBwcTEBAAwI0bNzh48CDLly9n+fLljB07llGjRuV8UCIiuYxGdxcREckHDMPgh70/8MryVwiLDgPgydpPMv7B8fh7+ts5utwhMVFPazq2Y8eOMXLkSObNm0ehQoXYuHEjderUydH4jh07RlxcHFWrVs3S8XFxcRw7doxChQpRpkyZFPtiY+HDD2HsWHOKNnd3eOcdGDoUcmL6+FatWrF27VpWr16dqnb566+/5rnnnsPZ2ZnTp0/bkvi87OTJk5QvX56WLVuyZs0ae4cjIrmARncXEREpQA5dOkSb2W14ctGThEWHUcW3CiufXsnszrOVoGdQxYoVmTt3Lv369ePatWv07dvXLjFkNUEHcHZ2pmrVqqkSdAAXF3jjDfj7b2jVCq5fh9deg7p1zXV7GjhwIGXKlCEuLo4tW7bYNxgRkVxASbqIiEgedT3uOm+seoPaX9Zm1YlVuDm5Mfb+sex5bg+ty7e2d3h50scff4yHhwe7du1iw4YNqfafPHmSgQMHUq5cOVxdXSlevDjdunXj77//TvecmzdvpkePHpQoUQJXV1dKlixJcHAw3333XYpy6fVJP3jwIE899RQVK1bEzc2N4sWLU6dOHYYOHUpISEiK2G7VD3r27Nn07duMHTu8cHEphKNjbQoVGofFciNV2T59+mCxWFizZg3r1q2jdevWFC5cGC8vLzp06MCBAwfS/bxZ4efnB5DmmADXrl3j3XffpWbNmri7u+Pt7U2LFi2YM2dOmueyWCyUK1cuzX0zZ87EYrHw9ttvp9ie2Gf+5MmTLF68mMaNG+Ph4YGPjw+PP/44Z8+eTfN8ly5dYuDAgQQEBFCoUCHq1q3Lt99+m+7nvHr1KpMnTyY4OJiyZcvi6uqKr68vbdu25c8//0zzmOSx/fDDDzRu3JjChQtTpEgR/vrrLywWC02bNk33mu+88w4Wi4WxY8emW0ZEchcl6SIiInmMYRgsOLCA6l9U5//W/x9x1jjaV27P/uf3M6rFKFydXO0dYq4QFxfH9OnTmT59OnFxcRk6xtvbm3bt2gGwevXqFPs2bNjAPffcw5QpU/D09KRjx45UrlyZhQsX0rhx41TlASZNmkTTpk356aefKFWqFF26dKFq1ars3LmTN95447bx7Ny5k/r16/P9999TvHhxOnfuTKNGjYiNjeWTTz7h8OHDGfpcAwcO5Omnn2bHjh00b96cjh07UKRICH/9NZLWrVtz/fp1/vkHPvjAbBqfaMmSJbRu3ZorV64QHBxMYGAgy5Yto0WLFoSGhmbo2rcTGRnJkSNHAKhWrVqqfS1atGD06NFcuHCBhx9+mKZNm7Jt2zYef/xxhg4dmi0xJPriiy/o2rUrhmHQtm1bPD09mTNnju1nlNzly5dp2rQpU6ZMwdnZmY4dO+Lt7c0zzzzDRx99lOb5t2zZwpAhQzh48CCVK1emc+fOVKlSheXLlxMcHMz06dPTjW3cuHE89dRTuLi48PDDD1OzZk0aNGhA/fr12bRpE/v37091jNVqZcaMGTg6OvLMM8/c2Q9HRHJOdHS0UZCWkJAQAzDCw8MNERGRvGZ3yG6j1cxWBm9j8DZGqQmljAUHFhhWq9XeoeU6MTExxttvv228/fbbRkxMjAEYwG2PGzt2rAEYjz/+uG1beHi4ERAQYDg7Oxs//fRTivJ//vmn4eLiYpQsWdKIiYmxbV+7dq1hsVgMLy8vY/Xq1ali+/3331NsK1u2bKr4evfubQDGggULUsV54MAB4/z587b3J06cMACjZcuWKcrNnz/fAIySJUsaR48eTfGZmjVrZgDGsGGvGu3aGQYYRlCQYTz4oHldBwcH44cffrAdEx8fb3Tt2tUAjDfffDOdn2BqLVu2NIAUP4fr168bu3fvNtq1a2cARseOHVMd98ILLxiA0aZNGyMyMtK2/eDBg4afn58BGEuXLk1xDGCULVs2zThmzJhhAMZbb72VZnweHh7GypUrbdujo6ON++67zwCMadOmpThmwIABBmA8+uijxo0bN2zbly1bZjg5OaX5b3H8+HFj48aNqeLauXOnUaRIEcPLyyvF50wem5ubm7FmzZpUx06ZMsUAjKFDh6ba99tvvxmA8cgjj6T58xCRnBMeHm4ARkhIyG1zVtWki4iI5AEXoy/yv1//R70p9Vhzcg1uTm682eJNDg06RJdqXQrcyO0Z4eTkRM+ePenZsydOThmf0KZYsWIA/Pvvv7Zt06dPJzQ0lGHDhtGtW7cU5du0acPzzz/PuXPn+PXXX23b33//fQzDYPTo0amaoLu4uBAcHHzbWC5cuABA69apuy9Uq1aNwMDA257j008/BWDMmDFUqlTJtt3Ly4svvvgCi8XC119/Rbdusfj7w5EjkNjy+uGHn+Dxxx+3HePo6MjIkSMBWLdu3W2vfbP777/fNgWbu7s7derUYcWKFYwePZp58+alKBsdHc20adNwcHDgiy++wNPT07avatWqtpYIiZ8vO7z00kspftaFChXilVdeAVJ+3qioKGbPno2TkxOffvoprq5JrVfatWtH9+ST1CdTvnx57rvvvlTb69aty6BBg4iIiEizRQZAv379aNmyZartTzzxBF5eXsyePZuYmJgU+7755hsAnn322fQ+sojkQkrSRURE7oK4OPjlF+ja1ZzuKsvnSYjjky2fEPRZEF/t+AqrYaVHjR4cGnSIMfePwcPFI/uCzmccHByoWrUqVatWxcEh43/yGP+N/p78wUdif+FOnTqleUyzZs0A+OuvvwBISEiwjeo9YMCAzIZuU79+fQCefvpptm3bhtVqzdTxiYOxWSwWnnjiiVT7a9WqRe3atYmMjKRWrT0cPgwvvQSJH/3XXx9i6FC4ciXpmKCgIIAU/eEzKjg4mN69e9O7d2+eeuopHnjgAVxcXJgwYQJff/11irI7duzg+vXrNGzYkMqVK6c611NPPQXAxo0b0xyxPyseeuihVNvS+rw7d+7k+vXrNGrUKM2B+pI/2LhZQkICy5cv5+233+a5556jT58+9OnTx5acHz16NM3jOnbsmOZ2Dw8PevXqxeXLl1m0aJFt+4ULF/jll18oUaIE7du3TzceEcl9NE+6iIhINvr7b5g501wSK2INA55/PnPnMQyDpUeX8uqfr3Lo0iEA6gTU4ZO2n9CibItsjVlSunTpEgA+Pj62bSdPngSgUaNGGTr20qVLXL9+HT8/PwoXLpzlWF599VU2bNjAkiVLWLJkCd7e3jRq1IiHH36YPn363Pbcly9fJjY2loCAANzc3NIsU65cOfbs2cP58+dp0AAmTIATJ2DxYrBaS/HJJ1C6NPxXoWyr0b651jYjXn/99VStCi5evEjbtm158cUXKVasmO1hwvnz523xpaVIkSJ4e3sTHh5um9roTpUqVSrVtrQ+b2JsaSXot9p+9uxZHn74Yfbs2ZNuDJGRkZk6J8Bzzz3Hl19+ydSpU3nssccAc5C8uLg4+vbti6OjY7rHikjuoyRdRETkDl26BD/8AN98A3v3gpMTJA5S7ehozkmdGVvObmH4iuGsO2U2ry1WqBjvtX6PvnX74uigP7Yzymq1cvr0aeDWCc7Ndu/eDUD16tVt2xISEgDo3r07hQoVSvfYm5P4O+2G4OXlxapVq9i4cSNLlixhzZo1rFy5kuXLlzNu3DjWr19PxYoVb3uejMSRvExivjt+vIW1a2HQoKRy/7XAzzbFixdnzJgxPPzww3z88cepavwzG/ut3K4lQkbPk1Zri4zo378/e/bsoUuXLgwfPpwqVapQuHBhHBwcmDJlCgMHDky3VUB6D1kAateubRu88NixY1SsWJFp06ZhsVjo169fpmIUEfuze5I+ZcoUJk2aRGhoKNWqVePDDz9MdxqJn3/+malTp7J3715iYmKoVq0aI0eO5MEHH8zhqEVEpKCLi4Pff4dp02DpUvgvhwOSEnQwmw1nNEk/fOkwo1aNYsHBBQC4OroypNEQRjYfSRG3ItkXfAERHx/PrFmzABgxYkSGjgkPD+f3338HzP7TiUqVKsXhw4d54403qF279m3PU6xYMdzd3QkLCyMyMvKOatMtFgvNmjWzNam/ePEiL774Ij/++CMjR45k7ty56R7r6+uLi4sLoaGhXL9+Hfc0voynTp0CSLN/e/36STXoYH63E38sWahIT1f58uUBUoxWX6JECQBOnDiR5jHh4eGEh4fj4eGR4ufr7OxMVFRUmsecOXMmW+JNjC3xZ3ezxIdDyUVHR/Pnn3/i7+/PvHnzUtVuHz9+/I5ieu6559iyZQvTpk0jODiYI0eO8NBDD6XbEkFEci+79kmfP38+r732Gq+99hqbNm3ivvvuo3PnzuneQDds2EDr1q1ZuHAhGzZsoEWLFnTv3t32xFtERORu27vXTFoCAqBjRzNBj483m7SnVQFmscD69fDss/Dii/D66/DOO/DhhzB5sln7/vm0qwSP/JrqL73CgmWX4GwjHi3yBn92OMGL1T/Eeq0I16+nfX5Jn8VioXjx4hQvXjzDNZ6vvPIK0dHRNGjQgCZNmti2t2nTBoDFixdn6DyOjo62Zt1Tp07NVNy3U7x4cds833v37r1lWWdnZxo3boxhGPz444+p9u/bt489e/ZQuHBh7rnnnttee/dusyk8QGgoPPII3KLldoYlJqgeHkljLNSvXx93d3e2bduWZj/txHnmmzVrluLfNzAwkMuXL3MleUf6/yxfvvzOg/0vNjc3N7Zu3Zrm361pzeEeHh6O1WolMDAwVYIeHx+foj95VvTo0YOiRYsyc+ZMvvzyS0ADxonkVXatSZ88eTK9e/emT58+AHz00UesXLmSqVOnMmbMmFTlb55z8p133mHp0qX89ttv1KlTJwciFhGRgujyZfjxRzOh3rPHbMKeWHOevNY8LXFxcOwYHD+eNBgXmAl3gtXAsFqAIsDA/xbTz/8tN3NxAVdXcHMzl0KFkhYPD3Nxd0+9FCqU9vZblXVzg0yMt5brODs783wGBwM4fvw4I0aMYN68eXh4eDBt2rQU+wcOHMiECRN47733KF26NH369EmRGEZHR7NgwQJat25t69c8fPhwfv/9d959910aNGhA8+bNbeXj4uJYtWrVbUd4/+qrrwgODrbVNCf67bffgIw14x88eDDr1q3jrbfeolWrVlSoUAEw+z6/8MILGIbBwIEDcXFxue257r3XHP29dGnz/a+/msvjj5sPn9IY3+22Ll68yFtvvQWQYoAzDw8P+vbty+eff86gQYNYtGiRLYk/cuQIY8eOtX2+5Fq2bMns2bN59913mThxImA2T3///ffZtGlT5gNMg6enJ7169WLatGm2Vg2JI7wvX7481Uj1AH5+fnh7e7Nv3z42btxoazmakJDAa6+9ZpsrPqvc3d15+umn+eSTT5g7dy7Fixfn0UcfvaNzioh92C1Jj42NZdeuXbZpLRK1bt2arVu3ZugcVquVyMhIihYtmm6ZmJiYFAN9pDcYh4iIyM0OHoRRo2DJkpTN2ZOvZ0T65TPfXzk21lxu9evMwcFcbn4oYLWaS2Y4O6d8KJCYxN/8UCAzDwFu9QAhJ8a3SqwcsFqtREREcOTIEQ4dOoRhGFSuXJkffviBWrVqpTimaNGiLFq0iI4dO9K3b1/eeecdatasiaurK6dPn+bgwYNER0eza9cuW5LesmVLPvzwQ1599VVatGhBw4YNqVixIhcuXGDPnj14eHjYBqRLz1dffcX//vc/qlevTrVq1XBycuLw4cPs3r0bd3d3W3J7K926dWPAgAFMmTKFmjVr0rp1awoVKsSaNWu4ePEijRs35p133snwzy9xbLWSJaFZM5g713yINW+e+RCrRo30j33//feZOXMmYP78Q0JC2Lx5M9HR0VSsWJH33nsvRflx48axZcsW/vzzTypUqEDLli2Jjo5m1apV3LhxgyFDhtChQ4cUxwwfPpz58+czadIk1qxZQ8WKFdm7dy9nzpzh+eef54s7mW7hps+ydu1aFi1aROXKlWnatClhYWGsXbuWgQMH2mqzEzk5OfHaa68xatQoWrZsSevWrfHx8WHr1q2EhYUxaNAgPv/88zuKaeDAgXzyySeA+T13dna+o/OJiH3YLUm/fPkyCQkJ+Pn5pdju7+/PihUrMnSOTz75hGvXrtGlS5d0y4wfPz7VDV9ERCQj1q+HO2yBahdZScbTExdnLul08QWy96GAk5P5UCDxwUB6DwVu10Kgbl1Ir/V2Yj91JycnvLy8KFGiBE8//TQdO3akY8eO6c6p3rRpU/bu3cuECRNYunQpq1atwtHRkRIlSvDwww/TpUuXFIPNAQwbNowGDRowceJENm3axK5du/Dz86N+/fo8/fTTt/15vPvuuyxevJitW7eycuVKYmNjKVWqFAMGDODVV19NMe/5rXz99dc0a9aMr776irVr1xIfH0/FihUZOnQoL730Upp91W/HyQnmzDG7cLzxhvngKPnHv3499XgMf/zxR4r3np6eBAUF0bFjR15++WW8vLxS7C9cuDBr167l448/Zu7cufzyyy+4uLhw77338vzzz6c51VmNGjVYtWoVI0aMYNu2bRw/fpymTZsyb948du3alenPmZ5ixYqxceNGRo0axS+//MLixYsJCgpi6tSptG7dOlWSDjBy5EhKlSrFpEmT2LhxI+7u7jRr1owxY8awc+fOO46pWrVqlChRgvPnz9O/f/87Pp+I2IclOjraLj3cQkJCqFSpEqtWrUoxEuqHH37Ijz/+eNub6Lx58xg0aBBz586ldevW6ZZLqyY9KCiI8PDwVL8IREREbrZvH3z0kTl6u2FkvhZdsl/iA4HkTfETxwSwWs3XatVgz544W9/gxx57TLWKd9m1a+ZDEzC7iFStCj16wPDhkInB9eUObNq0iaZNm9KyZUvWrFlj73BEJJnEqSJDQkJum4faraeZr68vjo6OhIWFpdh+4cKFVLXrN5s/fz7PP/88s2fPvmWCDuDq6oqXl5dtuZPRVUVEpOCpWRNmzTIHyxo61ExC8nI/7fzAajUfliTW8sfFmWMDJCQkDa5nsZj9kI8fP87x48fTndZKsk/ymekWLDCnJvziC6hUyRw48Q4HL5cMSGw9+sILL9g5EhG5E3b7M8PFxYW6deuyatWqFNtXr16dao7R5ObNm8fAgQOZMWMGbdu2vdthioiIAGY/3PHj4fx5GDcOihc3t9920HBLyqp3i8XA0dFsKuzsbC5OTmZf7DucUluS8fAwm7N37tyZzp07p9uEXe6OZ5+F1auhdWvzIco330BQEPTuDclmWZNssGnTJvr160ejRo1YunQp9evXv2VXUBHJ/ezW3B3MGvH+/fvzySef0KhRI6ZPn87MmTPZvn07ZcqUYfTo0Zw/f55vvvkGMBP0Z599lo8++oiOHTvazuPu7o63t3eGrhkREUFgYKCau4uIyB2JiTGbwL//vjnadfIR32/Wvvd+HmtTldgYR65f55bLtWsQHW0u166Zy40bSUtsbOb6eSc2C7dYkh4C3Nw0PD9q2RLU2jd32LQJ3n0X/pt+Hjc3CAmBIkXsGla+MXPmTJ555hkKFy5Mq1at+OyzzzI06r+I5KzMNHe3a5IOMGXKFCZOnEhoaCjVq1fngw8+oFmzZgAMGDCA06dP8/t/d/W2bduyfv36VOfo1asXU6ZMydD1lKSLiEh2slrhs++P8+7/xXHpcBWwxIGRsu/z0qWQbGapO2IYZs3krZL82z0IuN1DgevXzQcCMTHmkpl++Gk9FEiMOzsHtLud9u3Nn7vkHn/9BWPHgq8vTJ+etH3jRmjSRN1IRCR/y1NJek5Tki4iItkhwZrA0qNL+WTrJ6w68V/XrTON8N8zgbAdTXByhPh4M0tdtQruv9+Owd6h+Pg7exhwc9n0HgokPhi43dzzN7t5dPn4eOjaFebONaf4AggMDMRBWWCuEB9vdvEAc2DGWrXM+dVfeQWefjr1iPAiIvlBZpJ0ddASERHJhIiYCKbvms7kbZM5/q85EpajxZHuNbrz+sDXuSfgHo4eNfuvz5hh1nrn9TFLnZzMz5BTnyMhIesPABKXbt0gPj7e1mVuxIgRuLi45MwHkFtKPjzA4cNms/ejR+G558yp3AYNgoEDITDQbiGKiNiVatJFREQy4Ojlo0zeNpkZu2cQFWtOGl7UrSjP1nuWQQ0HUcY7dR/QCxfMWvQePdSU1x7i4uL4/PPPARg0aJCmYMuloqLM5u8TJ8LJk+Y2Jyfo0gUmT4bbTPojIpInqLn7LShJFxGRjIq3xvPb0d/4asdX/Hb0NwzMX5nVi1dnSMMhPFn7STxcPOwcpUj+EB8PCxfCp5+a/dT9/eH0aUhsAGEYmgFBRPIuNXcXERG5A2fCz/DNzm+Ytmsa5yLP2bZ3qNyBFxu9SJsKbbAoWxDJVk5OZquTHj1gzx44dSopQU9IgPr1oUULs1l89er2jVVE5G5STbqIiAhJteZTdk5h2dFlWA1zGPJihYrR554+DKg/gMq+le0cpUjB9Mcf0LZt0vvGjaFvX+jZE/TnnIjkBWrufgtK0kVEJLnDlw4z++/ZzNozi7MRZ23b7y93PwPqD6Bz1c64OrnaMULJqvj4eObPnw9At27dcHJSA8K8ymqFFSvgiy/g11+TpgUsVAi6d4fXX4eqVe0bo4jIrai5u4iIyC1cuX6FufvmMmvPLLae22rb7uvuS586Zq15kG+QHSOU7GC1Wjl8+LBtXfIuBwd46CFzCQ2F2bNh2jRzdPhZs+D555PKJiSAo6P9YhURuVNK0kVEpECITYjlt6O/8e3f37Lk8BLirHGAOX1acKVgnq79NJ2qdlKteT7i6OjIww8/bFuX/CEgAF59FYYNg82bYelSaNAgaf/AgeaUbk88Yday+/jYL1YRkaxQc3cREcm34q3xrDm5hnn757Hw4EIuX79s21cnoA5P136ax2s9ToBngB2jFJHsEhdnTtl29ar53tnZ7Mveqxc88ojZPF5ExB7U3F1ERAqsBGsC606tY+7+uSw4uIBL1y7Z9gV4BvBkrSd56p6nqO1f245Risjd4OwMf/8Nc+bADz/A7t2wZIm5eHrC0KHw7rv2jlJE5NaUpIuISJ4XlxDH+tPrWXBgAfMPzudC9AXbPl93X7pW60qPGj1oWa4lTg761VdQGIbBxYsXAShevLimzSsgSpc2m8O/+iocOGAm6z/8ACdOmH3bE127Bj//DB06aIR4Ecld1NxdRETypIiYCH7/53d+OfwLS48u5eqNq7Z9Rd2K0qVaF3rW6Emrcq1wdnS2X6BiN7GxsYwbNw6AESNG4JI46bYUOIYBW7ZAyZJQpoy5beFC6NrVnIv9wQehSxezSXzx4vaNVUTyJzV3FxGRfOlsxFl+OfwLvxz+hVUnVtkGfwNzPvNHgh6hR40ePFD+ASXmAkAhdUIWwGKBJk1SbktIgCpVzBHily41F4sFGjWChx+G/v3B398+8YpIwaaadBERybVi4mPYcHoDfxz7gz+O/cHfYX+n2F/ZpzKPVnmUR6s+SpNSTXB00AjeIpJxhgEHD8KCBWbN+u7dSfuOH4fy5c3106fB1xc8POwSpojkA6pJFxGRPMkwDP658g9/HPuD3//5ndUnV3Mt7pptvwULTUo3oWNQRx6t+ihVi1W1Y7QiktdZLFC9urm8+SacOwfLlpnJemKCDjB4MPz+OzRtCm3amM3j69XTfOwicneoJl1EROwqJDKEtafWsubkGpYfW86JqydS7A/wDCC4YjDBFYN5sOKDFCtUzE6RikhBZLXCPffAvn0ptxcpAq1bQ/v20K+fXUITkTxENekiIpJrhUaFsvbkWlafXM2ak2s4fPlwiv3ODs40K9OM4IrBtK3Ultr+tTUqt2RJfHw8v/zyCwAdO3bEyUl/9kjmOTiY07r98w/8+SesWAGrVplzsS9cCFeupEzS582DOnWgcmWzpl5EJLP020pERO4awzA49u8xNp/ZzMYzG1l7ai2HLh1KUcaChToBdWhVrhX3l7uf+8vfj6eLp50ilvzEarWyd+9eAB5++GE7RyN5mcViJt2VK8Pzz0N8POzYYSbs5collbt0CXr2NNf9/aF586Sldm01jxeRjFGSLiIi2SY6Nprt57ez+exmNp3ZxJazW7h47WKKMsmT8lblWtG8THOKuhe1U8SSnzk6OhIcHGxbF8kuTk7mKPCNGqXcfvGimZBv3QphYTB/vrmAORf7u+/CkCE5H6+I5C1K0kVEJEvirfEcvnSYHSE72HZuG5vPbmZP6B4SjIQU5VwcXagfWJ8mpZrQomwLmpdtjo+7j52iloLE0dGRxo0b2zsMKUCqVYN16+DGDfjrL1i/3lw2boSICChcOKnstm3w+ONmot+woflaty64udkvfhHJHZSki4jIbcUlxHHg4gF2huxkR8gOdoTsYE/oHq7HX09VtmThkjQp3YQmpZpwX+n7qBtQF1cnVztELSJiH25uSc3cwWwe//ffULp0UpktW8xp3o4fhx9/NLc5OZmD1NWrBy+8YDaRF5GCR0m6iIikcOnaJfZd2MfesL3su7CPXaG7+Dvsb2ISYlKV9XTxpG5AXbOm/L/EvLR36TTOKpLzDMMgPDwcAG9vbw1AKHbj5GQm3sn17g1Vq5o16lu3msvFi2Zf9x074Kmnksr+8gt8/71Z016njrkEBOTkJxCRnKQkXUSkgIqKjeLAxQO2ZHzfRTMxD4sOS7O8t6s39QLrUS+wHvUD61MvsB6VfSvjYHHI4chFMiYuLo5PPvkEgBEjRuDi4mLniESSeHvDQw+ZC4BhwKlTZjP53bvNGvVEq1ebo8bPm5e0rVixpDneR42CUqVyNHwRuYuUpIuI5GNWw8rZiLMcvnSYI5ePcPhy0uvJqyfTPa5C0QrU9KtJLb9a1PavTf3A+pQvWl4JueQ5zs7O9g5BJEMsFnOk+HLloHv3lPueeAICA83kffduOHzYHEl+3TpzGT06qey4cbB0qZm816hh1tZXqgRly5o1+iKS++m/qohIHmc1rIREhnD83+OcuHoiRTJ+9PLRNPuNJwrwDKCWXy1q+tW0JeXVilfTFGiSL7i4uDBy5Eh7hyFyxxo0MJdE166Zifr+/XD0aMqm71u2mAPVbdyY8hzOzlC+PGzeDD7/jd159Kg5LVzZspoeTiQ3sURHRxv2DiInRUREEBgYSHh4OF5eXvYOR0QkQ/69/i8nrp7gxL8nbMn4iavm+qmrp9LsL57I2cGZij4VCfINoopvFar4ViHIN4hqxatRrFCxHPwUIiJytx08aNa2HzhgJvFHjsA//0BMDLi7Q3S0WWsP0LUrLFxoJvCJtfhlyya9PvaYat9FsktERATe3t6EhITcNg/VfzsRETuLjInkbMRZzkSc4WzEWduS+P5M+BnCY8JveQ5HiyOlvUtTvkh5gnyDkhLyYlUoV6QcTg663YuIFATVqplLclYrnDtnLsnHTzQMcHU1E/ijR80lkZsb9OqV9H7wYDPxL1cOypSBkiWhRAnztWRJ8PVNeW4RyTr91SYichcYhkF4TDhhUWGERoUSFm2+hkaFEhYVxrnIc7YkPCImIkPn9Pfwp3zR8pQv8t9StDwVilagfJHylPYurURc5Cbx8fEsW7YMgPbt2+OkKkEpoBwczOnfSt80+cbChWYCf/asORXcyZPm4HUnT0JCQsqke/Nmc9T5tCTW0CcaPx5CQpKS+MBA8Pc3lyJFlMyL3I5+W4mIZND1uOtcvn6ZS9cucfnaZS5fv8zF6Iu2BPzmRPxWTdBvVsStCKW8SlHKqxSlvUrb1hOXst5l8XDxuIufTiT/sVqt7Nq1C4C2bdvaORqR3MnBwawZL1Pm1uU++8ysaT95Es6cMWvlz583X29OvOfMST+h9/U1B71LNGEChIaaCbyfX9JrsWJm3/lChe70E4rkPUrSRaRAMQyDqNgowmPCuXrjKuE3wgmPCefK9Sspku/L1y9z+dp/Cfl/67cagC09Xq5eBHgG4O/hb3v19/SnZOGSlPY2k/GShUtS2LXwXfi0IgWbo6Mj999/v21dRLKucWNzSUt8fMr3zz0Hhw4lNbEPCzOX8HAoWjRl2e+/h5070z5v0aJw5UrS+1dfNWv8fXzMxdc36dXXF1q0yPrnE8lNlKSLSJ5gNaxEx0YTFRuV5hIeE25LuK/euJoqCU++bjWsWY7DycEJX3dfihUqhm8h8zXAIwB/T/+UybinP/4e/rg7u2fjT0FEMsPR0ZEW+qtd5K67uSdJ//5pl7txAyJu6uH17LPm4HZhYXDhQtLr5ctJo9AnWrUq/YS+SBH499+k98HBsG2bOR+9tzd4eSWt+/rCp58mlV23zozLy8tcPD3BwyPp1UGzj0oOs3uSPmXKFCZNmkRoaCjVqlXjww8/pGnTpumWX79+Pa+//joHDx4kMDCQl156if7p3QlEJEdYDSs34m9wPe461+Ov217T2pZ837W4a+km3VGxUUTHJSXl1+KuZWvMjhZHirgVwdvNG29Xb3zcfcyk291MvpMn4r7uvraEvLBLYSzqTCciIpJpbm7mktxzz6Vd1jDg+k0N2MaMMfvMX7liJvHJXz1vmjn0yhW4etVcbla0aMokfcwYWLky7TicnCA2Nqk5/4svwtatKZN4T8+k9bffTprObtMm86GDu7v5uW9+LVVKDwAkbXZN0ufPn89rr73GpEmTaNy4MdOmTaNz587s2LGD0jePbAGcPHmSLl260KdPH6ZNm8aWLVsYOnQoxYoVo1OnTjn/AURygGEYJBgJxFvj011iE2KJTYglJj7Gth6bEEtMQsr3GS5z07aY+BhuxN8wk+40Eu7YhNgc+3k4WBzwdPG0LR7OHni6eOLl6mUm3a7eeLt533a9kHMhJdsi+ZxhGFy7Zj7gK1RI/+dF8hKLJXV/9A4dMn78r7+aNevh4eYSEZG0fvOtoEqVpH2RkeYgeFFR5oMCD4+U5Q8cMJP0tDg4mAl/ovHjYdGi9GOMjk76jP36wU8/pUzkk68vWmS2AgCYORPWrwcXF3N0fheXpMXVFf73P7NFAMD27eZYAsn3Jy9fs2bSg5PwcLh2zXwwkdaiW2jOses86S1btqROnTp88skntm316tXj4YcfZkzyb/h/3njjDZYtW8bOZO1chgwZwt69e1m9enWGrpkf5kk3DAMDI8Wr1bCm2paVV6thveNzZHc8VsNKgjUhad1IyHXbE4wEEqxmIh1njbtlQp2RJS4h6RwJRoK9v3KZ4uTghLuTO+7O7ile3ZzcUm1zd3KnsGvhNJPu9BY3Jzf9oS0iGRIbG8u4ceMAGDFiBC4uLnaOSETyCsMwm+dfu2Y2j0+0fbs5YF5UVFIyn7geFwcff5xUdsQIsyn99evmuW5+vXYtqSa9e3eYPz/9eCIioPB/w9f07QszZqRf9vx5c0R9gCFDYPLk9MsePQqVKiXF+/776ZfdvRvuucdcHz/eLOvsnHZC/913SWXnzYOvvkpd1tHRXEaNMh8WAKxdCz/+aG53cEgqk7g8/XTSFIN795oPYxwdYcAAs8tDbpYn5kmPjY1l165dvPLKKym2t27dmq3pPJ7atm0brVu3TrGtTZs2zJo1i7i4OJydnVMdExMTQ0xM0gjLkZGR2RD93Td7z2z6/tI3VdIqksjB4oCTgxOOFkdcnVxxcXSxLa6OKd+7OLpkrMxN25If4+romiLJdnNyS5WMuzm5aRowERERyfMslqTa7OTuvTfj5/jvGWGGfPmlWf769ZTJfOJ68lYF3bpB5cpmM/zEJSYmaT150//KlaF165T7k5dP3v3AMMyENyGd+qHkqVZkpNnVID2xyRpZnjoFt6pPHTAgaX3fPvj66/TLNm2alKTv2AEjR5rr3bvn/iQ9M+z21/Tly5dJSEjAz88vxXZ/f39WrFiR5jFhYWH4+/un2Obn50d8fDyXLl0iMPGRUTLjx4/nvffey77Ac4jVsBJvjb99wWxkwYKDxQGLxYIFyx29Olgc7vgcifE4OjiarxbzNfm2O96ejed0cnBKtTg7Oqe5PbOLs0PK8yReW0RE0ufi4sJbb71l7zBERG6rWDFzyYj27c0lIwYPNpeMeP99czEMM1GPjzdbB8THm0vykfkHD4aePVOXSXxfpUpS2UcegdKlU+6PiwOr1bxO5cpJZRs2hHfeSdp381KhQlLZSpXMVgUJCUmtDPILu1d53dxs1TCMTDVlNQwjzfMkGjZsGIOTfTMjIyMJCgrKQqQ5q1v1brSp0CZTyeydJMQiIiIiIiIWS1KT9JsH+kuUmYcKVauaS0Y0aGAuGdGsmbnkR3ZL0n19fXF0dCQsLCzF9gsXLqSqXU/k7++fqvzFixdxcnLCN3lnkWRcXV1xdXXNnqBzkIeLBx4uHvYOQ0RERERERHKQ3drLuri4ULduXVatWpVi++rVq2nUqFGaxzRs2DDVAHErV66kXr16afZHFxEREREREclL7NqpdfDgwcycOZNZs2Zx6NAhXnvtNc6cOWOb93z06NEp5kDv378/p0+fZvjw4Rw6dIhZs2Yxa9YsXnzxRXt9BBEREREREZFsY9c+6d26dePKlSu8//77hIaGUr16dRYuXEiZMmUACA0N5ezZs7by5cqVY+HChQwfPpwpU6YQGBjI+PHjNUe6iIiIiIiI5At2nSfdHvLDPOkiIiIiIiKSd2RmnnTN4SQiIiIiIiKSSyhJFxEREREREckllKSLiIiIiIiI5BJ2HTjOHgzD7IIfERFh50hERERERESkIEjMPxPz0VspcEl6VFQUAKVLl7ZzJCIiIiIiIlKQREVF4e3tfcsyBW50d6vVSkhICJ6enlgsFnuHc0uRkZEEBQVx5MgRChcubO9wJA/Qd0YyQ98XySx9ZySz9J2RzNJ3RjIrr3xnDMMgKiqKwMBAHBxu3eu8wNWkOzg4ULJkSXuHkSmFCxfWdHGSKfrOSGbo+yKZpe+MZJa+M5JZ+s5IZuWF78ztatATaeA4ERERERERkVxCSbqIiIiIiIhILqEkPRdzdXVl5MiRuLq62jsUySP0nZHM0PdFMkvfGcksfWcks/SdkczKj9+ZAjdwnIiIiIiIiEhupZp0ERERERERkVxCSbqIiIiIiIhILqEkXURERERERCSXUJIuIiIiIiIikksoSbejKVOmUL16dXx8fGjatCkbN268Zfn169fTtGlTfHx8qFGjBt98800ORSq5RWa+M+vWrcPDwyPVcvjw4RyMWOxpw4YNdOvWjYoVK+Lh4cGSJUtue4zuMwVbZr8zus8UbB999BHNmzfH39+fsmXL0rNnT44cOXLb43SfKbiy8p3RfaZgmzp1Kg0bNiQgIICAgADuv/9+/vjjj1sekx/uMUrS7WT+/Pm89tprvPbaa2zatIn77ruPzp07c+bMmTTLnzx5ki5dunDfffexadMmXn31VYYNG8bixYtzNnCxm8x+ZxLt3r2bY8eO2ZZKlSrlUMRib9HR0dSqVYsJEyZkqLzuM5LZ70wi3WcKpg0bNjBgwABWr17NkiVLiI+Pp2PHjkRHR6d7jO4zBVtWvjOJdJ8pmEqWLMmYMWNYv34969evp2XLlvTs2ZMDBw6kWT6/3GM0BZudtGzZkjp16vDJJ5/YttWrV4+HH36YMWPGpCr/xhtvsGzZMnbu3GnbNmTIEPbu3cvq1atzJGaxr8x+Z9atW0e7du04d+4cRYoUycFIJTfy8PBgzpw5PPLII+mW0X1GksvId0b3GUnu4sWLlCtXjj/++INmzZqlWUb3GUkuI98Z3WfkZqVKleL//u//6N27d6p9+eUeo5p0O4iNjWXXrl088MADKba3bt2arVu3pnnMtm3baN26dYptbdq0YefOncTFxd21WCV3yMp3JtF9991HhQoVaN++PWvXrr2bYUoep/uMZJXuMwIQEREBQNGiRdMto/uMJJeR70wi3WckISGBn376iejoaBo2bJhmmfxyj1GSbgeXL18mISEBPz+/FNv9/f0JCwtL85iwsDD8/f1TbPPz8yM+Pp5Lly7dtVgld8jKdyYgIIDPPvuM77//nh9//JGgoCA6dOjAhg0bciJkyYN0n5HM0n1GEhmGweuvv859991HjRo10i2n+4wkyuh3RvcZ2bdvH35+fhQtWpQXX3yRH3/8kWrVqqVZNr/cY5zsHUBBZrFYUrw3DCPVtlsxDCPN80j+lZnvTFBQEEFBQbb3jRo14uzZs3zyySfpNikTuZnuM3Irus9Iopdffpl9+/axYsWKTB+r+0zBlNHvjO4zEhQUxObNmwkPD2fx4sUMHDiQ33//Pd1E/WZ58R6jmnQ78PX1xdHRMVUN6IULF1LVlCZKq8b04sWLODk54evre9dildwhK9+ZtDRs2JBjx45ld3iST+g+I9lB95mC55VXXmHp0qX89ttvlCxZ8pZldZ8RyNx3Ji26zxQsLi4uVKxYkXr16jFmzBhq1qzJF198kWbZ/HKPUZJuBy4uLtStW5dVq1al2L569WoaNWqU5jENGzZMNdjBypUrqVevHs7OznctVskdsvKdScuePXtSNQESSaT7jGQH3WcKDsMwePnll/n5559ZtmwZ5cqVu+0xus8UbFn5zqRF95mCzTAMYmJi0tyXX+4xau5uJ4MHD6Z///7UrVuXRo0aMX36dM6cOUP//v0BGD16NOfPn7fN69e/f3++/vprhg8fzjPPPMPWrVuZNWsWM2fOtOOnkJyU2e/MZ599RtmyZalWrRqxsbHMmTOHxYsX88MPP9jzY0gOioqKSlHTcPLkSfbs2YOPjw+lS5fWfUZSyex3RveZgu2ll15i3rx5zJ07F09PT0JDQwHw9vbG3d0d0N8zklJWvjO6zxRsb731Fg899BClSpUiMjKS+fPns379etuUavn1HqMk3U66devGlStXeP/99wkNDaV69eosXLiQMmXKABAaGsrZs2dt5cuVK8fChQsZPnw4U6ZMITAwkPHjx9OpUyc7fQLJaZn9zsTGxjJy5EjOnz+Pu7s71apVY8GCBbRt29ZeH0Fy2M6dO2nXrp3t/euvvw5Ar169mDJliu4zkkpmvzO6zxRsU6dOBUj17/3VV1/x1FNPAfp7RlLKyndG95mC7cKFC/Tv35/Q0FC8vLyoWbMmixcvts14lF/vMZonXURERERERCSXUJ90ERERERERkVxCSbqIiIiIiIhILqEkXURERERERCSXUJIuIiIiIiIikksoSRcRERERERHJJZSki4iIiIiIiOQSStJFREREREREcgkl6SIiIiIiIiK5hJJ0ERGRfObUqVN4eHiwZ8+ebDnf//3f/9G4ceNblhkwYAA9e/a8ZZl169bh4eHB1atXb3vNhx56iLlz52YmzExr3rw5P//88129hoiISGYpSRcREblLBgwYgIeHBx4eHnh7e1OjRg1GjBhBdHR0ho7PTFJ7N7344ossXbo0U8e0bduWV199NUvX++233wgLC6N79+5ZOj6jXn/9dUaPHo3Var2r1xEREckMJekiIiJ30YMPPsixY8fYv38/o0ePZurUqYwcOdLeYWWKp6cnvr6+OXa9L774gieffBIHh7v7Z0rbtm0JDw/nzz//vKvXERERyQwl6SIiIneRq6srAQEBlCpVip49e9KzZ0+WLFkCgGEYTJgwgRo1auDr60ujRo1YtGgRYDZZb9euHQAlS5bEw8ODAQMGALB8+XLatGlDiRIlKF26NF27duX48eMZjunLL7+kQYMGtvdLlizBw8ODr7/+2ratY8eOjB49Gkjd3D0hIYHhw4fbrj9q1CgMw7DtHzBgAOvXr+eLL76wtSQ4deqUbf+uXbto1qwZxYoVo3Xr1hw5csS279KlS6xevZoOHTqkiPnq1au88MILlCtXDh8fH+69915+++03AGbPnk2JEiX47bffqFOnDsWKFaNXr15ER0fz3XffUa1aNUqWLMkrr7xCQkKC7ZyOjo4EBwfz008/ZfhnJyIicrcpSRcREclB7u7uxMfHA/DOO+/w3XffMen/27u3kKi6Po7j3/GQx/KQTuMBD1lkqCiaCOpIFtSVZFSQUZEURJEIdqGFGRFRYMVj2lylCJGV0OEiFCoKnMFDaUkXaYSJDEVSYQqaocz7XoSb5q2ntCefhPf3gQHZe63/WrNu5L//e6356y+6u7s5dOgQe/fuxW63Ex0dTVNTEwC9vb0MDAxQXV0NwMTEBCUlJbS1tXHnzh08PDzYvn37rF/btlqt9PX18f79ewDsdjthYWE4HA4Apqen6erqIjc397v9a2pquHz5MjabjXv37jEyMmI8eACorq4mKyuL4uJiBgYGGBgYIDo62rh/4sQJTp8+jd1ux8vLiwMHDhj3Ojo68Pf3JzEx0bjmcrnYvHkznZ2d1NfX09PTw8mTJ90q7RMTE9hsNhobG7l9+zZ2u52ioiLu3r3LzZs3uXTpEg0NDcZDkBlr1qyhvb19VusmIiLyb/D60xMQERH5f9Hd3U1zczNr165lfHyc2tpaWlpayMrKAiA+Pp6Ojg7q6+uxWq2EhIQAEB4eTnBwsBGnsLDQLa7NZiMuLo6+vj6SkpJ+Oo+Zyr3D4aCwsBC73U5JSQl1dXUA9PT0MDk5SXZ29nf7X7x4kcOHDxvzuHDhAvfv3zfuBwUFsWjRIvz8/LBYLN/0P378OFarFYCysjK2bNnC5OQkvr6+DA0NYTab3RLwBw8e0N3dzZMnT1i5cqWxVl+bmpqipqaG5cuXG2t09epVBgcHCQwMZPXq1eTl5dHW1sbWrVuNfpGRkTidTlwu17y/Xi8iIjIb+m8kIiIyj1pbWzGbzYSGhpKfn09OTg5nz56lv7+fyclJCgoKMJvNxqepqYnBwcEfxnz16hV79uwhKSkJi8ViJOZOp3NWczKZTOTk5GC32/n48SN9fX3s27cPl8tFf38/bW1tpKWlERgY+E3f0dFR3r59azxYAPDy8iI9PX3Wa5KcnGz8PZPEv3v3DoBPnz7h6+vr1v7Zs2dERUUZCfr3+Pv7Gwk6gNlsJjY21u07mM1mY5wZvr6+uFwuPn/+POv5i4iIzCdV0kVEROZRXl4eNTU1eHt7ExERgbe3N4CxR/vGjRtERka69fHx8flhzG3bthEVFUVdXR0RERG4XC4yMzOZmpqa9bysVisNDQ20t7eTkpJCcHAwOTk5OBwO7Ha7UemeDzNrAF8eGADGq/phYWGMjIy4tffz85tTzJm4Xl5e31z73y0BIyMj+Pv7z2oMERGRf4Mq6SIiIvMoICCAhIQEYmJi3BLJxMREfHx8cDqdJCQkuH1m9m8vWrQIwO2wsw8fPtDf3095eTn5+fkkJib+0k+0zexLv3XrlpGQ5+bm8vDhwx/uRw8KCsJisfDo0SPj2vT0NE+fPnVr5+3t/Us/bZaamsrw8LBbop6cnMzr1695+fLlnOP9zPPnz0lLS/vtcUVERH6VKukiIiJ/wOLFiyktLaWiogKXy0V2djZjY2N0dXUREBDAzp07iYmJwWQy0draysaNG/Hz8yMkJISlS5fS0NCAxWLB6XQap7DPxcy+9OvXr9Pc3Ax8SdyPHDkC8Lf70QEOHjzI+fPnWbFiBatWraK2tpbR0VG3NrGxsTx+/JihoSECAgIIDQ2d1bxSU1MJCwujs7PTON3earWSm5vLjh07OHPmDAkJCbx48QKTycSGDRvm/N2/1t7ezvr16/9RDBERkd9JlXQREZE/pKqqioqKCs6dO0d6ejqbNm2ipaWFuLg44MuhZpWVlVRVVREfH09ZWRkeHh40NjbS29tLZmYm5eXlnDp1as5jm0wmo1o+k5CnpKQQFBREamoqS5Ys+du+paWlFBUVsX//ftatW0dgYCAFBQXftPH09CQjI4PY2NhZ75f39PRk9+7dXLt2ze36lStXyMjIoLi4mIyMDCorK3+pUv+1N2/e0NnZya5du/5RHBERkd/JND4+/p+fNxMRERH5dwwPD5OZmYnD4SAmJmbexjl69ChjY2PGqfYiIiILgSrpIiIisqAsW7YMm8026+r7rwoPD+fYsWPzOoaIiMhcqZIuIiIiIiIiskCoki4iIiIiIiKyQChJFxEREREREVkglKSLiIiIiIiILBBK0kVEREREREQWCCXpIiIiIiIiIguEknQRERERERGRBUJJuoiIiIiIiMgCoSRdREREREREZIFQki4iIiIiIiKyQPwXGLKmWu4HMUcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1200x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_range = np.linspace(0,3,1000).reshape(-1,1)\n",
    "y_proba = logis_reg.predict_proba(X_range)\n",
    "\n",
    "mid = None\n",
    "for i in range(len(X_range)):\n",
    "    if y_proba[i,1] - y_proba[i,0] <= 0.000001:\n",
    "        mid = X_range[i,0]\n",
    "\n",
    "%matplotlib inline\n",
    "fig, ax = plt.subplots(1,1, figsize=(12,3),\n",
    "                       facecolor='whitesmoke',\n",
    "                       edgecolor='gray')\n",
    "ax.plot(X_range, y_proba[:,1],'g-',label=\"Iris-Virginica\")\n",
    "ax.plot(X_range, y_proba[:,0],'b--',label=\"Not Iris-Virginica\")\n",
    "ax.vlines(mid, 0, 1,lw=1.5, ls=':', color='gray')\n",
    "ax.annotate(text=\"Decision Boundary\", xytext=(mid,0.2), xy=(mid-0.4,0.2),\n",
    "            arrowprops = {'headwidth':10,'facecolor':'b','edgecolor':'b'},fontsize = 15)\n",
    "ax.annotate(text=\"\", xytext=(mid,0.9), xy=(mid+0.4,0.9),\n",
    "            arrowprops = {'headwidth':10,'facecolor':'g','edgecolor':'g'},fontsize = 15)\n",
    "ax.set_xlabel(\"Petal width(cm)\")\n",
    "ax.set_ylabel(\"Probability\")\n",
    "ax.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4129efa4",
   "metadata": {},
   "source": [
    "# Softmax Regression\n",
    "1. also called Multinomial Logistic Regression\n",
    "2. ova combinations\n",
    "3. combination function - normalized exponential\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "    s_{k}(x) & = & \\theta^{T} \\cdot x \\\\\n",
    "    \\hat p_{k} & = & {\\sigma[s(x)]}_k = \\frac{exp[s_{k}(x)]}{\\sum_{j=1}^{K}{exp[s_{j}(x)]}}\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "4. here $\\theta$ is a $(k,m)$ matrix, k means k-classes and m means m features, $x$ is still a $(m,n)$ data matrix with each column symbolizes one data entry, final output $s_{k}(x)$ is a $(k,n)$ matrix\n",
    "5. for training, all target should be processed into one-hot form, then \n",
    "6. cost function (similar to logistic regression, instead of binomial distribution, it's a multinomial distribution)\n",
    "$$\n",
    "    J(\\theta) = -\\frac{1}{m}\\sum_{k=1}^{K}{y_k \\cdot log(\\hat p_{k})}\n",
    "$$\n",
    "7. derivitive form of cost function\n",
    "$$\n",
    "    \\frac{\\partial J(\\theta)}{\\partial \\theta_{k}} = \\frac{1}{m}[\\hat p_{k} - y_{k}]\\cdot x\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "0f05a557",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(C=10, multi_class=&#x27;multinomial&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(C=10, multi_class=&#x27;multinomial&#x27;)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial')"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# select 2 different features: petal length, petal width\n",
    "X_sft = raw_iris[\"data\"][:,(2,3)]\n",
    "# 3 classes, and will be transferred into one-hot form\n",
    "y_sft = raw_iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class='multinomial',solver=\"lbfgs\", C=10)\n",
    "softmax_reg.fit(X_sft,y_sft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "59c509a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x176c72e10>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx_sft = np.linspace(0,7,100)\n",
    "yy_sft = np.linspace(0,3.5,100)\n",
    "\n",
    "xx, yy = np.meshgrid(xx_sft, yy_sft)\n",
    "zz = np.zeros_like(xx)\n",
    "for x_idx in range(len(xx_sft)):\n",
    "    for y_idx in range(len(yy_sft)):\n",
    "        zz[x_idx, y_idx] = softmax_reg.predict([[ yy_sft[y_idx],xx_sft[x_idx]]])\n",
    "\n",
    "fig,ax = plt.subplots(1,1,facecolor='whitesmoke',edgecolor='grey',\n",
    "              figsize=(8,3))\n",
    "#ax.scatter()\n",
    "ax.contourf(xx,yy,zz,cmap=plt.cm.autumn_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0628d564",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "315.594px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
